help-0

[lone heart]

✅

[small lance]

They actually have a real question in another channel

But yes, I shouldn’t have closed it before getting consent

[still herald]

don't encoach upon multple channel

s

[lone heart]

@lean rose Has your question been resolved?

Channel closed

Closed by @lean rose

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unreal phoenix]

Help

[unreal phoenix]

During a meeting, n-people are sitting around a round table. They all disperse for lunch break and come back after an hour to resume the meeting. In how many ways can they sit around the table so that no one sits immediately to the left of someone they sat immediately to the right of before leaving for lunch?

Say the initial arrangement is 123...n

Can someone verify my answer?

[lone heart]

@unreal phoenix Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tight pier]

Is there a way to integrate $$\int_0^a \arcsin(x) : \dd x \quad 0 < a \leq 1$$ without using integration by parts?

[ocean seal]

𝔸dωn𝓲²s

[buoyant saddle]

i don’t know but why would you want to

ibp for the inverse trig functions is pretty simple

[tight pier]

I got this challenge from a friend and I can't seem to find a proper substitution or something, so I would like to know if somebody got any hints.

.close

[lone heart]

Channel closed

Closed by @tight pier

Use .reopen if this was a mistake.

[livid sage]

yes but it's only feasible if a = 1, sqrt3/2, 1/2, etc (values for which you can calculate arcsin(a))

[tulip marsh]

weierstrass substitution?

[tight pier]

I figured it out

I made a change of coordinates

so simple goddamn

[tulip marsh]

To polar?

[tight pier]

no

i send photo

.reopen

[lone heart]

✅

[tight pier]

but who cares

.solved

[lone heart]

Channel closed

Closed by @tight pier

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[inner finch]

Hi everyone.

I don't know where to start with this summation.

$S(n)= \sum_{k=0}^nk(k+1)$

I only know the formula for the sum of the first natural numbers (Gauss' formula)

What are the steps to solve this one?

PS: please excuse any mistakes in my English, I'm Italian

[ocean seal]

Shadow91518

[livid sage]

you can use this

[buoyant saddle]

and the one for just k

1/2(k)(k+1)

[inner finch]

Thank you.

Even if the index is k=0?

[livid sage]

well 0^2 = 0 so nothing changes

[inner finch]

so how should I rewrite this summation?

only the first step, after that I try to solve

[mortal trellis]

multiply out k(k+1)

[lone heart]

@inner finch Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[delicate geyser]

Hello, could someone explain why ai = ai-1 + ai-2 + ai-3

[mortal trellis]

the string is either of the form .....11 or .....101 or .....1001. each of those is counted by one of the a_i

because for example the one ending in 101 is a string of length i-2 ending in 1 plus the string 01

so for each allowed string of length i-2 you get exactly one such string ending in 101

[delicate geyser]

why cant it be of form say ....00

[midnight osprey]

.close

[mortal trellis]

oh whoops thats from the previous one that they have to end in 1

[delicate geyser]

ooh okay

[mortal trellis]

ok second answer, slightly different but same idea

wait no sry

[delicate geyser]

okay i think I get it

if u delete the last 1 from 11 you get all the ones ending in 1 and similarly with 101 and 1001

by taking away 01 and 001

yeah thats what you said

[mortal trellis]

yeah thats from the second answer but its for the recursion for P(n)

the a_i dont have the requirement of ending in 1

[delicate geyser]

yeah

[mortal trellis]

but similar idea. it either ends in 1, 10 or 100. by cutting those off you get an allowed string of length i-1, i-2 or i-3

[delicate geyser]

oh yes

okay I got it now thank you

.close

[lone heart]

Channel closed

Closed by @delicate geyser

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[delicate citrus]

So for step 2, I did 117.2 minus 90 to get 27.2. So now looking at the big triangle, and pretending I cut a line down the middle, I have 90 degrees, 27.2 and for step 3 Id use the pythag theorm which is all sides should equal to 180. So 90 plus 27.2 =117.2 so the last missing angle is 117.2. Now, Im stuck on step 4, where I have to find the missing side length there, i dont how what to do to find that

[delicate citrus]

forgot a step, I would do 180 minus 117.2 to get 62.8 to be the last angle on the top part

[lone heart]

@delicate citrus Has your question been resolved?

[delicate citrus]

no..

I think I figured it out, just need someone to help me confirming the degrees bc if those are wrong then everything is wrong

[lone heart]

@delicate citrus Has your question been resolved?

[delicate citrus]

No..

I need help

[lone heart]

@delicate citrus Has your question been resolved?

[delicate citrus]

No I need help..

[fathom kite]

@delicate citrus so whats ur angle

do u know the law of sines?

[delicate citrus]

No but ive heard of it

[delicate citrus]

I think its 27.2 but id like someone else to confirm it

[sly cedar]

is the other angle opposite 27.2

[delicate citrus]

i have 62.8, 90 and 27.2

I want to confirm that 27.2 is correct

since if thats wrong I dont believe my further calcs will be right

[sly cedar]

27.2 is correct

117.2-90 = 27.2

[delicate citrus]

Ok,

[sly cedar]

do you know how to find the missing side

do you know the law of sines

[delicate citrus]

no but can I find the height first by doing this,

[delicate citrus]

Not rlly

height =9.11?

Does this work?

@sly cedar

[sly cedar]

yeah

pretty sure

[delicate citrus]

erm

ok, then area of triangle = 1/2 base times height so,

id just do 17.5 times 9.11

and not need to divide by 2 since 1 triangle is added to the other

@sly cedar can u explain the law of sines rq

[sly cedar]

in a triangle with points ABC and side lengths abc

an angle and it's opposing side that are known can be used to find an unknown angle or side using their opposite angle/side

[delicate citrus]

Ok

[sly cedar]

you can use it in ur question with the topmost angle of the triangle

and it's opposing side is 35ft

which is the length of the base of the triangle

[delicate citrus]

yeah but i cut that triangle half to be 17.5

So what do I do next @sly cedar

oh nvm when you use law of sines you look at the entire triangle

[lone heart]

@delicate citrus Has your question been resolved?

[delicate citrus]

not rlly

[delicate citrus]

.close

[lone heart]

Channel closed

Closed by @delicate citrus

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[strange fractal]

Excuse me

can i have help with dis

[lone heart]

@strange fractal Has your question been resolved?

[small lance]

Damn, why are you always doing Math?

Have you learnt reflection matrix?

[strange fractal]

noo not always

ive been playing games for 3 hrs

LOL

IM ON THE GRIND

[strange fractal]

yes

[small lance]

Alr, tell me how it works

[strange fractal]

um

the formula! :D

[small lance]

Alr. Do you know what does theta stands for in the matrix?

[strange fractal]

um

angle

@small lance

[small lance]

What angle?

Could you elaborate it?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[small lance]

.reopen

[lone heart]

✅

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pseudo badge]

Can someone help me rearrange pls 😔

I got k=3 but I’m not sure at all

[lone heart]

@pseudo badge Has your question been resolved?

[lone heart]

@pseudo badge Has your question been resolved?

[lone heart]

Channel closed

Closed by @pseudo badge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fresh cliff]

What graph will be formed on round(√(a-b)) such that a & b are natural numbers < 10001 and a > b. (3 dimensional coordinate plane).

[lone heart]

@fresh cliff Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[proper radish]

Hi

[proper radish]

So im trying to understand this proof of heine borel, namely every open cover has a finite subcover implies that K is bounded and closed. How can we be sure that the finite subcover does not march to infinity?

Like, suppose K is an open interval (0, infty) because we havent shown bounded, then my finite subcover here must be infinitely many, no?

[dark breach]

(0, infty) is not bounded

[lone heart]

@proper radish Has your question been resolved?

[pallid scarab]

since {x1,...,x_n} is a finite set, we can find the maximum distance between every point

name it D

since every point of K is at a distance of at most 1 from one of them

there's a distance of at most 1 + D + 1 between every point in K

(1 is to go from the first point to the closest open ball

the other 1 is to go from the closest open ball center to the second point

and D is to go between ball centers)

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[frigid yarrow]

if i have a line in space , will i get the direction vector of the line using 2 points of the line ?

[frigid yarrow]

@alpine sable what do you mean by that mate ?

.close

[lone heart]

Channel closed

Closed by @frigid yarrow

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[raw jetty]

in trapezium ABCD, BAD=ADC=90°, diagonals AC and BD are perpendicular, AB=sqrt7 and BC=sqrt217, find ad

[raw jetty]

choices are
sqrt31
sqrt35
sqrt42
sqrt46
none of the avove

[lone heart]

@raw jetty Has your question been resolved?

[lone heart]

@raw jetty Has your question been resolved?

[small lance]

set coordinates

btw, congrats for getting helpful

[raw jetty]

thanks

what should i set as the origin?

[small lance]

Set D

Set AD as k, which is a variable

[raw jetty]

ok

hmm what next? cant seem to think about anything that i couldve gotten by using coordinates unfortunately, any hints?

[small lance]

Can I check what you have proceed so far?

[cinder tundra]

Have you tried finding DC?

[raw jetty]

im not sure what to start

[raw jetty]

not yet, lemme try

[small lance]

try setting cord B with k

[raw jetty]

b would be (sqrt7,k)

[small lance]

correct

how about line BD

do you have any idea?

[raw jetty]

$y=\frac{k}{\sqrt{7}}x$

[ocean seal]

Skill_Issue

[small lance]

yes

how about line AC?

remember, line BD and line AC are perpendicular

[raw jetty]

$y=-\frac{\sqrt{7}}{k}x+k$

[ocean seal]

Skill_Issue

[raw jetty]

i think

[small lance]

decent

can you find cord C with the given info?

CD is x axis

[raw jetty]

i think its $(\frac{k^2}{\sqrt{7}},0)$

[ocean seal]

Skill_Issue

[small lance]

yes

now you have B and C

what can you do next?

[raw jetty]

uh is it wierd i dont know

i can find bc maybe

[small lance]

yeah

that's correct

the given info mentioned that BC = sqrt217

Plus, k represents the length of AD

which is also wat you are looking for

[raw jetty]

i got $y=-\frac{k}{\frac{k^2}{\sqrt{7}}-\sqrt{7}}}(x-\sqrt{7})+k$

[small lance]

what is this for?

[ocean seal]

Skill_Issue
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[raw jetty]

for BC?

or am i using it incorrectly

wait oh you want me to use pythag right

[small lance]

no, I was referring to the length

length formula

[raw jetty]

right

[small lance]

which determine the distance between two points

[raw jetty]

$\sqrt{k^2+(\frac{k^2}{\sqrt{7}}-\sqrt{7})^2}}=\sqrt{217}$

[ocean seal]

Skill_Issue
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[small lance]

correct

proceed

[raw jetty]

$$k^2+(\frac{k^2}{\sqrt{7}}-\sqrt{7})^2}=217$$
let $a=k^2$
$$a+\frac{a^2-14a+49}{7}=217$$
$$a+\frac{a^2-14a+49}{7}=217$$
$$a^2-7a+49=1519$$
$$a^2-7a-1470=0$$

[ocean seal]

Skill_Issue
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[raw jetty]

how can i solve this quadratic without a calculator 😭

[small lance]

you have two options from now

[raw jetty]

wait this is multiple choice

[small lance]

a. factorize it

b. start plugging the given solutions

I prefer the latter XD

[raw jetty]

its either 42 or 46 cause 31 and 35 are too small

[small lance]

is it?

[raw jetty]

.

is it sqrt42

[small lance]

correct

[raw jetty]

i think it works

[small lance]

My work, it’s for reference

[raw jetty]

oo ok, thank you

.close

[lone heart]

Channel closed

Closed by @raw jetty

Use .reopen if this was a mistake.

[small lance]

Congrats getting helpful again

[raw jetty]

thank you very much!

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[radiant flax]

Does this hold?

[lone heart]

@radiant flax Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[analog garnet]

I don't know how they get from (1) to (2). Can anyone provide a demonstration of that?

[lone heart]

@analog garnet Has your question been resolved?

[lone heart]

@analog garnet Has your question been resolved?

[lone heart]

@analog garnet Has your question been resolved?

[somber yarrow]

x² - 6x - 41 = 0

i need helpp

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lone heart]

Please don't occupy multiple help channels.

@river osprey Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wraith stirrup]

.

[wraith stirrup]

i have ton find the convergence interval

i used root test and got

lim (n->infinity) of x/n

but if i plug infinity i got 0

and for root if result is smaller than 1: the serie is converges but what is the interval than ?

<@&286206848099549185>

[alpine sable]

!15min

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[wraith stirrup]

oww oke

[alpine sable]

no worries, just a little fyi

[pseudo ice]

Remember that for the root test, if you're doing the "general" version, you want the values such that the limit of your |x/n| is less than 1, but you deduced that for any choice of x, the limit becomes zero, right?

[wraith stirrup]

the thing that i thought is

the value of x could be anything

but like in other excercices i got as result x

but here i got a number so does this mean that it is convergent for every reel numbe or not

[pseudo ice]

It is convergent for all real numbers, yes

[wraith stirrup]

ok thanks

.close

[lone heart]

Channel closed

Closed by @wraith stirrup

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unkempt urchin]

the ans for this question is 5040 but can anyone explain how to get that value through working?

[cerulean vector]

do you know how to find the number of ways to arrange if all 3 were together?

[unkempt urchin]

yes

[cerulean vector]

how would you do that

[unkempt urchin]

6!/3! x 7?

[cerulean vector]

how did you get this?

[unkempt urchin]

i found the all the possible arangments for the letters other than G then i multiplied it by all the possible positions the 3 G's can occupy

am i wrong?

[cerulean vector]

did you group all 3 G's as one?

[unkempt urchin]

yes

[cerulean vector]

you could do the same for 2 G's and then subtract the number of cases where all 3 are together

[unkempt urchin]

wait i dont understand could u explain a bit

[cerulean vector]

group 2 G's together as (GG) R E E N A G E
find the number of permutations of this

there would be some cases in which all 3 G's are together and that's what you need to exclude

[unkempt urchin]

ohh ok

tysm i understand now

.close

[lone heart]

Channel closed

Closed by @unkempt urchin

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[desert jackal]

How to do this? I don't know how please help me

[cerulean vector]

what are you supposed to do here?

[tight ocean]

Yeah, what are we supposed to evaluate?

Is there any context to this?

Are you multiplying like 5*(-1/3)p(2/5)*q?

If so then make a common denominator and you can distribute. Like 15/3 for 5. X E.

[desert jackal]

@tight ocean It is converted to root form

[tight ocean]

If it is in root form what do you want done, it should be about as simple as it gets right?

Oh, roots, as in powers, sorry. X E.

[desert jackal]

Can't you?

[tight ocean]

Actually now that I know it is powers, I guess it can be simplified, but sorry but I can't help you much. X E.

[desert jackal]

It doesn't matter

[lone heart]

@desert jackal Has your question been resolved?

Channel closed

Closed by @desert jackal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tight ocean]

I guess use a calculator for 5 to power -1/3. X E.

[lone heart]

Please don't occupy multiple help channels.

[tight ocean]

.close

[lone heart]

Channel closed

Closed by @tight ocean

Use .reopen if this was a mistake.

[tight ocean]

I think there is a glitch, I was trying to message old occupier and it still says my name, it should say your name Astra. Problem, hope you find a solution. X E.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[royal scarab]

Hey all, is this answer correct? If not, where is the mistake?

Find a δ for f(x) = x^4 with limit a^4
Solution:

ε > |x^4 - a^4|
or, ε > |x^2 + a^2| * |x + a| * |x - a|
or, (ε)/(|x^2 + a^2| * |x+a|) > | x - a |

Now,
AxAε: ε > (ε)/(|x^2+a^2|)*|x+a|) > |x-a|
So ε = δ [i.e. any ε can be a δ]

[lone heart]

@royal scarab Has your question been resolved?

[lone heart]

@royal scarab Has your question been resolved?

[royal scarab]

<@&286206848099549185> Help, please!

[real gazelle]

Seems like you started with ε and used that to conclude a value for δ. For this to work, you need to set δ to be something in terms of ε and then use that to prove that |x^4 - a^4| < ε.

Also I don't see why this inequality is true

ε > (ε)/(|x^2+a^2|)*|x+a|)

Or how you concluded this

ε = δ

[royal scarab]

Because ||x^2+a^2|*|x+a| is positive

Oh actually

It could be <1

[real gazelle]

yeah

[royal scarab]

Thanks

[real gazelle]

You should probably choose your δ to take that into account. But of course δ can't depend on x (only a and ε).

[royal scarab]

.close

[lone heart]

Channel closed

Closed by @royal scarab

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[final tundra]

you have 7x - 8y = 2, knowing that (6 , 5) is a solution, solve for the rest of the solutions.

[final tundra]

where x and y are integers

i'm getting into this type of math after studying basic calculus stuff

[small lance]

There are infinite solutions

[royal scarab]

y = 2 mod 7 suffices

[final tundra]

and for x?

[final tundra]

also i gotta get used to seeing "mod" and actually knowing what it means 😭

[small lance]

Parametric function would work

If you’re looking for a function that concludes every solutions

[final tundra]

nah it's good

.close

[lone heart]

Channel closed

Closed by @final tundra

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[heavy prairie]

Help me someone please help me

[heavy prairie]

f(sqrt 5 + 2) = (6/x) - 2x

I start by putting the funny x value where the x's are

[boreal jetty]

Hello what is the question

[heavy prairie]

I keep getting it wrong and I can't find my way out it is a maze and endless maze

[boreal jetty]

Take a screenshot of the question please.

[heavy prairie]

It is in Swedish

[boreal jetty]

It's fine.

[heavy prairie]

they want me evaluate f(x) at x = (sqrt5 + 2)

and f(x) = (6/x) - 2x

[wraith stirrup]

plug than just the value of x in the function

[boreal jetty]

can you take a screenshot of the question maybe?

[heavy prairie]

bro I wrote the question down but I can definitely SHOW MY WORK

[boreal jetty]

Okay ...

[heavy prairie]

did this step go wrong

[wraith stirrup]

$$f(sqrt 5 + 2) = (6/x) - 2x$$

[ocean seal]

LikiKush

[wraith stirrup]

and what cant you find ?

put in calculator and its done

[heavy prairie]

it isnt a calculator question

[wraith stirrup]

put than everything on the same denominator

[heavy prairie]

that might work actually i will try that and get back to you

[boreal jetty]

you can probably simplify what you showed us

fraktion

[heavy prairie]

yeah idk i got stuck

<@&286206848099549185> i probably did something illegal

[fiery rain]

you forgot to put - before 8sqrt5

[heavy prairie]

nooooo

😦

okay i will try again

thanks harry

[fiery rain]

👍

[heavy prairie]

yeah u are totally right it is so obvious when someone points it out

i got stuck but i have decided i will revisit the problem tomorrow i have been doing math for a while now and im getting tired

thanks for the help anyway

.close

[lone heart]

Channel closed

Closed by @heavy prairie

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wraith stirrup]

find the convergence: (-3)^n/n*3^n

[wraith stirrup]

$$frac{(-3)^n/n*3^n}$$

[ocean seal]

LikiKush

[unique dune]

${\frac{(-3)^n/n*3^n}}$

[ocean seal]

:D
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[unique dune]

${\frac{(-3)^n}{(3n)^n}}$

[ocean seal]

:D

[unique dune]

this?

[wraith stirrup]

no n not square^n

${\frac{(-3)^n}{n*(3)^n}}$

[vestal shell]

You can start by simplifying the expression

[ocean seal]

LikiKush

[wraith stirrup]

i tried

[vestal shell]

(-3)^n = (-1)^n * (3)^n

[wraith stirrup]

i got 1/n

[vestal shell]

So you would get (-1)^n / n

[wraith stirrup]

yes i got this also

used than leibniz rule

[unique dune]

isnt this

[wraith stirrup]

and got 1/n

[unique dune]

alternate harmonic

[vestal shell]

Yes

It converges

[wraith stirrup]

yes it is

but 1/n

i used p-test

and p = 1 so divergent ? no ?

[vestal shell]

Leibnitz rulee yes

[unique dune]

not for alternate

[vestal shell]

For alternating series

1/n

Diverges yes

I don't remember exacly what leibnitz rule tells you

[wraith stirrup]

and what are the conditions for alternate series if it converges or diverges

[vestal shell]

Let me see

Limit of the expression goes to 0

And it is a decreasing expression

Which is not the case

[unique dune]

bro

alternate harmonic converges

[vestal shell]

So by leibnitz you cant tell that the expression converges

[wraith stirrup]

im confused rn

[vestal shell]

Yessss

It converges

[wraith stirrup]

bro wait

[unique dune]

so, what are we tryna do

[wraith stirrup]

i first used alternating series

and than we can use the other test to prove diverges/converges

but i used p-test

and got tha for p-test in diverges

what does that mean than ?

[wraith stirrup]

for the absolut value of a(n)

[unique dune]

u just use alternate

cuz

p-test is usually for all positive ones

when u see alternate, u just check whether the sequence is decreasing or not

[wraith stirrup]

ow wait

cuz i used alternate to get a positive serie and than used other test to prove the diverges/converges of this positive serie

so i just check the conditions and if they are completed it means that he positive serie and the absolute serie is converges right ?

.close

[lone heart]

Channel closed

Closed by @wraith stirrup

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[twin epoch]

Nr 38, find AB by just knowing that DE is parallel to AB and that DE is 8 cm. How do I do this?

[livid sage]

similar triangles

[twin epoch]

Yeah this is too easy compared to other stuff on this server

.close

[lone heart]

Channel closed

Closed by @twin epoch

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

Given the identity...
determine (A + B)n

[wind cloak]

why don't you just like

substitute values for theta

[alpine sable]

That's not what I am supposed to do

[wind cloak]

put θ = 0 and you get A = 1

[wind cloak]

you enjoy doing this?

[alpine sable]

I do it, bc I want to improve my math skills

[wind cloak]

alright

[alpine sable]

Do you have any hint?

[livid sage]

restart from here

factor the 6th powers using difference of cubes, not difference of squares

[alpine sable]

Ok, I'll do that

[alpine sable]

Thanks a lot 👍

.close

[lone heart]

Channel closed

Closed by @keen maple

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[summer dirge]

cross-posting here for more visibility
#1260424130822541403 message

[quasi vector]

I am gonna heroically step up and say that your proof/solution is incorrect

but I won't tell you why

[summer dirge]

it is not even my proof for once

lol

[quasi vector]

the proof given in the book is wrong

[summer dirge]

[lone heart]

@summer dirge Has your question been resolved?

[lone heart]

@summer dirge Has your question been resolved?

[summer dirge]

.solve

.solved

[lone heart]

Channel closed

Closed by @summer dirge

Use .reopen if this was a mistake.

[summer dirge]

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[naive terrace]

hi

[naive terrace]

i have a questio

question

i have this linear equation in 2 variables

3x+4y-72=0

and i need to find the maximum value of xy which lies on this line

there positive

yeah

theyre

[teal crag]

what da haill

oh nah fanum tax abouta eat that

[naive terrace]

i dont know x+y

can i use the point of intersection of these

[limpid turret]

Calculus can do this

[naive terrace]

i do not understand it

i have not studied it yet

i can try understanding basic boundary line calculus

[ocean seal]

Yorkshire

[naive terrace]

got it

this method slipped out of my mind

thanks

.close

[lone heart]

Channel closed

Closed by @naive terrace

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[summer dirge]

cross-posting one of my proofs again
#1260424130822541403 message

[lone heart]

@summer dirge Has your question been resolved?

Channel closed

Closed by @summer dirge

Use .reopen if this was a mistake.

[summer dirge]

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mystic nebula]

so g(f(2))?

[hushed locust]

since they are continuous, yes

[mystic nebula]

so id do g(5)

which would be 2

got it

[lone heart]

@mystic nebula Has your question been resolved?

Channel closed

Closed by @mystic nebula

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[idle thorn]

Hello

[idle thorn]

I am confused on what the solution means

This is the question

This is the answer

But I don’t know what the answer means

[lone heart]

@idle thorn Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mild delta]

Add an appropriate middle term to complete a quadratic trinomial that can be factorised over Q

Show the correct factorisation:
x^2 (term placeholder) -32

[ocean seal]

Amir

[subtle birch]

basically you have product of two numbers to be -32

now b is the negative of sum of those two numbers

so you can find any possible pair of rationals that satisfy xy=-32

for your convenience, you may chose integral values

[lone heart]

@mild delta Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wanton juniper]

whats the answer

[twin nimbus]

!noans

[lone heart]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[twin nimbus]

Using the method of isoclines you should be able to find the answer easily

And I'm happy to help explain that

[wanton juniper]

Yes please

I do not get isoclines

[twin nimbus]

So an isocline is a stationary value

It's a value where the derivative is 0, and as a result the value never changes as time passes

So we have dp/dt = 7p - 4p^2

Our isoclines are when the function is stationary meaning what equation holds? @wanton juniper

[wanton juniper]

Uh

0 = 7p - 4p^2

?

[twin nimbus]

Yes

And what are the values of p where this is true?

[wanton juniper]

0

and

1.75

[twin nimbus]

Ok, based on this, can we eliminate an answer?

[wanton juniper]

A?

[twin nimbus]

Exactly

Ok what is the difference between B and C?

[wanton juniper]

Looks like C is just B but negative

[twin nimbus]

Ok so if we plug in a specific value of p, would we be able to distinguish the two cases?

[wanton juniper]

yes

[twin nimbus]

What value do you propose?

[wanton juniper]

1

[twin nimbus]

Sure try that

[wanton juniper]

so

1 is equal to 3

[twin nimbus]

What is equal to 3?

[wanton juniper]

7p - 4p^2

[twin nimbus]

Ok, how can we use that then?

[wanton juniper]

3 is a positive slope

[twin nimbus]

Yes, dp/dt is positive at p = 1

Meaning

[wanton juniper]

its b?

[twin nimbus]

Yep

[wanton juniper]

Nice

[twin nimbus]

👏

[wanton juniper]

Can u help me with the contiunation

of the problem

Sorry

[twin nimbus]

Sure

[twin nimbus]

!show

[lone heart]

Show your work, and if possible, explain where you are stuck.

[wanton juniper]

Uh

So

For (b) I do not know what lim p(t) is referring too

Idk if its the equation 7p - 4p^2

Or the graph we just answered

[twin nimbus]

The equation is a differential equation

You solve a differential equation to get a family of functions that are solutions for the differential equation

[wanton juniper]

Ok

[twin nimbus]

So the graph shows a bunch of those functions all at the same time

[wanton juniper]

Ohhhh

Would the limit be 1.75

Like from the last questio

[twin nimbus]

Yes, or more specifically 1750, because it's talking about population

[wanton juniper]

Oh Ok

So the population at 2000 will decrease towards 1750

[twin nimbus]

Sorry, p(t) will be 1.75

And the population will be 1750

It asks about both

[wanton juniper]

Oh

Ok

[twin nimbus]

Because of course it does

[wanton juniper]

For the question

Is it possible for a population of 2000 to decrease to 1600

[twin nimbus]

Ok, so in order for that to happen, you would need to cross what special value?

[wanton juniper]

1.75

or 1750

[twin nimbus]

Exactly, is that possible?

[wanton juniper]

no

Ahhh

Okay thank you

My problem is solved

.close

[lone heart]

Channel closed

Closed by @wanton juniper

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[toxic fable]

hi

[alpine sable]

hi

[nimble fern]

any math question to ask?

[toxic fable]

yep

idk where im going wrong

[nimble fern]

any work done so far?

[toxic fable]

we can extend af

to point x

where bx is perpendicular to ex

ax = 40 since cos eaf = 0.5

so fx = 8

notice fcx and fba are similar triangles

and that aecf = aex - cfx

bx = ae = 20

bf = sqrt(400 - 64) = 4root21

ab = 4root85 by pythagoras

by solving for all needed values using pythagorean theorem and similarity of triangles

[livid sage]

sm1 posted this exact question not long ago 👀

[toxic fable]

we get aecf = aex - cfx = 40root85 - 4root21

which is apparently incorrect

i dont see where i went wrong

[toxic fable]

where?

[livid sage]

this is wrong

[toxic fable]

oh

why

[livid sage]

cannot assume bx is 20

[toxic fable]

but ab is parallel to dc

and bx is perpendicular cx

[nimble fern]

why -4root21?

like how did you get cfx=4root21

[livid sage]

this is also an assumption

[toxic fable]

by similarity

[livid sage]

you are assuming lines EC, AF, and BX are collinear (which is false)

[toxic fable]

fc = bf/4 = root 21

[toxic fable]

oh

I guess i took the diagram to seriously

how would i approach this then?

and is there a way to prove they're not collinear or do we just assume not collinear until proven otherwise

[nimble fern]

we dont need to link BX

[toxic fable]

oh i think i got it

[nimble fern]

(and we are not sure if EX is perpendicular to BX)

[toxic fable]

fx is 8?

[nimble fern]

yea

[toxic fable]

fc = 8/root 3?

[nimble fern]

yep

[toxic fable]

ex = 20 root 3?

so why is my answer wrong

aex = 200root3 right

wait i got it

[toxic fable]

thank you boss

.close

[lone heart]

Channel closed

Closed by @toxic fable

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[opal gulch]

surely it has to be 4 comparing with 1

but the options are 1,2,3 or none of the above

and none of the above is wrong

[forest marsh]

If you need help in physics, its better to ask there https://discord.gg/physics
Here are mostly math help, you have better chance to have someone who will answer on the physics server

[hushed locust]

remember that an ideal wire will have no voltage drop

[forest marsh]

And that the voltage drop across all resistors in parallel is the same

[lone heart]

@opal gulch Has your question been resolved?

[livid sage]

🤔

people ask physics questions here all the time. and a bunch of people who hang around these channels are also well-versed in hs/early college physics

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lucid aurora]

hello, i know this is a simple equation but i just don't know exactly how to start solving it. any tips would be appreciated

[lucid aurora]

isn't it just 4^3?

[stuck ether]

yes

[lucid aurora]

okay

[stuck ether]

good luck

[lucid aurora]

this is a silly question then lol

thank u :))

[stuck ether]

no question is silly :)

[lucid aurora]

.close

[lone heart]

Channel closed

Closed by @lucid aurora

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[uncut tide]

hi can someone help me through this whole question

ive done a lot of stuff but it dsnt rly make sense

[cinder temple]

what lvl is this

[uncut tide]

first year uni

[cinder temple]

dam I'm second year and haven't lesrnt this

[torpid mirage]

did you start ?

[uncut tide]

well its maths fro physics so not pure maths

[uncut tide]

kinda but it got very confusing

[torpid mirage]

you can ask about what is confusing you

[uncut tide]

mostly the parts where its like a in negative and positive

[torpid mirage]

like part a for example

you gotta check 3 cases

[uncut tide]

ok

is there taykor expansions inveolved or not

[torpid mirage]

i don't think you will be able to do taylor, the function isn't defined at zero

[uncut tide]

ahhhhh ok yeah makes sense

whats the best way to wrtie down a as positve and negative

like thats where im confused

this is what i did before

does it make any sense

[torpid mirage]

you substituted, it works. honestly you can just leave it as it is and keep in mind it's negative

like whenever you work through the solution treat it as negative and that would be it

[uncut tide]

ok

but does it go to infinity for both it being negative and positive

[torpid mirage]

you mean small argument ?

[uncut tide]

yeah for a

[torpid mirage]

honestly yes

i wouldn't stop at that though

if you assume the argument is so small that $\alpha x << 1$ then you can even describe what the function looks like for small argument

[ocean seal]

Mohamed Mohsen

[uncut tide]

ahh ok

[torpid mirage]

it will behave as if $\alpha$ was zero.

[ocean seal]

Mohamed Mohsen

[uncut tide]

but dont we already have a bit asking what happens if a=0

[torpid mirage]

yes we do and nothing prevents them from being similar

in fact regardless of what alpha is, the first part always behaves as $\frac{1}{\sqrt{x}}$

[ocean seal]

Mohamed Mohsen

[torpid mirage]

for small arguments

[uncut tide]

ah i see

cool

so i can state that these all act very similar, like 1/sqrtx at small x

[torpid mirage]

yes

[uncut tide]

cool ok, so onto b

[torpid mirage]

great

[uncut tide]

oh, and they all go towards infintiy

[torpid mirage]

you mean b ?

[uncut tide]

for a, for small argument they go towards infinity

[torpid mirage]

yes they do, I would prefer you say they all act like $\frac{1}{\sqrt{x}}$, it holds more information than just saying infinity.

[uncut tide]

ok cool

[ocean seal]

Mohamed Mohsen

[uncut tide]

got it

for when a is positive , we have 1/sqrtx(1+ax)

so we have 1/(sqrtx+ax^3/2)

so if x is getting larger its going to act like 1/(ax^3/2)

[torpid mirage]

yes

and here you will notice how the sign of alpha will make a difference

[uncut tide]

yeah

[torpid mirage]

so all three cases will be different in that case

[uncut tide]

this goes towards 0, the first case

[torpid mirage]

they will go towards zero in all cases, but differently

[uncut tide]

hm yeah

[torpid mirage]

you gotta explain how differently they do

[uncut tide]

this one is positive

so its coming from the right??

[torpid mirage]

depends on how you graph it xD

if it's on the y axis it comes from above

so yes it approaches from the right i think

limit wise

[uncut tide]

cool , yeah it apporcahes from the right as its going to be positive getting smaller and smaller

this is where it got confusing before

[torpid mirage]

$f_{\alpha}(x) \to 0^+$ as $x \to +\infty$ is the mathematical way to write it i think.

[ocean seal]

Mohamed Mohsen

[uncut tide]

cool

[torpid mirage]

that's for positive alpha

[uncut tide]

yeah for negtaive it comes from the left

[torpid mirage]

yes

here is another confusing part what about zero ?

[uncut tide]

cool, ok now for 0

it approaches 0 too

[torpid mirage]

yes but is it different ?

or same

as the first case for example

[uncut tide]

same? but its 1/sqrtx

[torpid mirage]

yes, it has a different order

to make the answer perfect, keep that in mind in your answers

[uncut tide]

yeah, nice

ok cool , looking a lot neater than last time

[torpid mirage]

great !

[uncut tide]

ok so for c

vertical asymptotes, thats when the demoninator=0

[torpid mirage]

yes

[uncut tide]

so ill just do that or each case

[torpid mirage]

yes

[uncut tide]

so for a>0

x=0 and x=-1/a

[torpid mirage]

think about that again

[uncut tide]

(1+ax)(sqrtx)=0

[torpid mirage]

okay

[uncut tide]

sqrtx=0, 1+ax=0

[torpid mirage]

you get two answers yes but you gotta use your understanding

are both of these possible ?

[uncut tide]

ok

em, im guessing sqrtx is not

[torpid mirage]

uhmmm okay xD

[uncut tide]

no?

[torpid mirage]

sqrt one is a valid one

[uncut tide]

ah

[torpid mirage]

look

[uncut tide]

ok so why isnt the other one

hm

[torpid mirage]

if you write the question correctly

[uncut tide]

is it cos u cant have a negative

under a square root

like if i subbed this x back in

thats not a real solution

[torpid mirage]

find the limit points $x$ of D where D is the domain of $f$ at which there is an asymptote

yes that's correct

so you gotta take the points only if they are in the domain

[uncut tide]

ahhhhh

[torpid mirage]

well even the actuall points aren't in the domain xD but they are limit points to the domain

so they can be asymptotes

the other one doesn't have the function defined around it

so it can't be

[ocean seal]

Mohamed Mohsen

[uncut tide]

ok

so for case 2

[torpid mirage]

yes

[uncut tide]

sqrtx(1-bx)

x=0

xb=1

x=1/b

[torpid mirage]

b = - alpha right ?

[uncut tide]

sorry ive used my sub

alpha=-b

[torpid mirage]

it's okay you can do it

i just wanna make sure i understand

yes that makes sense

[uncut tide]

nws

and these are all valid

[torpid mirage]

yes they are

what about alpha = 0 ?

[uncut tide]

sqrtx=0

x=0

again

[torpid mirage]

great so it's similar to case 1

[uncut tide]

yeah, and 2?

does 2 not have an x=0

[torpid mirage]

why not ?

[uncut tide]

(1-bx)(sqrtx)=0

1-bx=0

x=0

[torpid mirage]

so you do

[uncut tide]

yeah

cool

[torpid mirage]

but two is different because

there is one extra

[uncut tide]

ahhhhh

[torpid mirage]

it's the only one that has an extra asymptote

[uncut tide]

yeah forgot

[torpid mirage]

and tie the loose ends, did you notice two was the only one that approached zero from the left as well ?

[uncut tide]

case 2

[torpid mirage]

yes

[uncut tide]

ah cool

[torpid mirage]

only case with an extra asymptote and only case approaching 0-

maybe it's not a coincidence

you will realize what that means in the next part of the question

because you gotta sketch it

[uncut tide]

ok, so can we go onto d

[torpid mirage]

yea

[uncut tide]

this is where is topped last time it got quite onfusing but i understand it more not i think

[torpid mirage]

yes the thing is you can't solve d on its own

you had to have solved all previous points

because you will use past results to sketch in d

[uncut tide]

yeah kinda annoying but yeah

[torpid mirage]

it's fun to me xD

i like interconnected questions

[uncut tide]

yeah if u get them right, its horrible if u cant do one part in the exam and it just keeps coming

anyway

for case 1

[torpid mirage]

yea i understand if you fail one part you faill the whole thing

[uncut tide]

a>0

[torpid mirage]

okay

make a sketch and show me

[torpid mirage]

that's great

xD

[uncut tide]

so for 2, what is going on in the bit between the asymptote

[torpid mirage]

yea i want you to figure it out

[uncut tide]

ahaha ok

[torpid mirage]

it's probably the hardest one

xD

[uncut tide]

ok so im gonna do rh an lh limits

[torpid mirage]

you are smart

[uncut tide]

so im thinking this will go to infinty

as we have a (1-1)

[torpid mirage]

left or right ?

[uncut tide]

basically

well thats where i got confused last time, and aslo the first time i thought of rh and lh limits the whole question aha

ok so

im doing it from the rh first

[torpid mirage]

we kinda were doing it the whole question xD

[torpid mirage]

so x coming from top

[uncut tide]

ik but when i did it myself

[torpid mirage]

okay

[torpid mirage]

I barely helped you though

i think you just needed a confidence boost

[uncut tide]

what do u mean coming from top, is it not just coming from rsh

[torpid mirage]

yea coming from the right sorry directions xD

[uncut tide]

nws aha

[torpid mirage]

okay is it infinity or -infinity ?

[uncut tide]

yeah thats what im trying to figure out

so coming from rhs, approaching 1/b from values basically bigger than 1/b

[torpid mirage]

true

[uncut tide]

the (1-xb) part, wil be negative till it gts to 1/b

becase x will be bigger than 1/b and we are subratcing

[torpid mirage]

great

so ?

[uncut tide]

so -infinty

im gonna write that all down now aha

[torpid mirage]

alright go ahead xD

[uncut tide]

ok for lhs

[torpid mirage]

What did you get for lhs

[uncut tide]

positve infinity

hm, so are we gonna have like , an arch looking thing in the middle

we know that, for small x, it goes to + infinty

[torpid mirage]

Is it all gonna be above zero ? That arch

[uncut tide]

it approches 0 rom lhs , its whats happening around zero in the bit inbetween the asymptote

[torpid mirage]

Lemme put that here so we don't have to scroll up

[uncut tide]

ok aha

[torpid mirage]

You can see that in the arch part. It's not really approaching zero but it's always positive

[uncut tide]

ok, how

so when a>0 but a<1/a