help-36

[solid cobalt]

But you have to substitute "2+h" in both cases

What changes is the branch you choose

[gentle zephyr]

for 2^+ we use first for 2^- we use second case of the piecewise then

[solid cobalt]

Yes

[gentle zephyr]

a moment bitte

[solid cobalt]

Kein problem

[gentle zephyr]

im making a mess here I need more help though

[solid cobalt]

You didn't read

And you lack the "lim"

[gentle zephyr]

,, \lim_{h \to 0^-} \frac{e^{(2+h-2)} - 1}{5 \cdot \left(2+h-2\right)}

0/0 tho

[solid cobalt]

You didn't substract 1/5 in the numerator, did you?

I'm lost the denominator is always "h"

Maybe you did some intermediate steps

[gentle zephyr]

einen moment bitte

[solid cobalt]

And h→0^-

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[gentle zephyr]

maybe we need to lhopital this shit no?

[solid cobalt]

??

What is to lopi?

Did you write it well?

I still can't see 1/5 substracted and h in the denominator

[gentle zephyr]

problem is I am trying to figure out f(x + h)

I thought taking left and side limits of 0 was needed here

[solid cobalt]

$$\lim_{h\rightarrow 0^-}\frac{\frac{e^{2+h-2}-1}{5(2+h-2)}-\frac{1}{5}}{h}$$

[gentle zephyr]

ohhh

so we need to take both sides of the limit for the coeficiente incremental

[soft zealot]

Categorist

[solid cobalt]

That's the so-calles left derivative at x0=2

Check if it is equal to the right derivative

[gentle zephyr]

yeah

one moment

thing is

[gentle zephyr]

but this is in 0/0 form, how do I evaluate this limit

$\lim_{h\rightarrow 0^-}\frac{\frac{e^{\left(2+h-2\right)}-1}{5 \cdot (2+h-2)}-\frac{1}{5}}{h}$

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[solid cobalt]

Derivative limits are always 0/0 bc f(x+h)-f(x) tends to 0 and h tends to 0

[gentle zephyr]

got it, so now what?

[solid cobalt]

If you don't get 0/0 at the first evaluation you did something wrong

$\lim_{h\rightarrow 0^-}\frac{\frac{e^h-1}{5h}-\frac{1}{5}}{h}$

[soft zealot]

Categorist

[gentle zephyr]

right

[solid cobalt]

Oh, did I do something wrong?

[gentle zephyr]

no

its correct

[solid cobalt]

Oh it is 0^+

[gentle zephyr]

$\lim_{h\rightarrow 0^+}\frac{e^h-1}{5h \cdot h}-\frac{1}{5 \cdot h} \\implies \lim_{h\rightarrow 0^+}\frac{e^h-1}{5h \cdot h}-\frac{h}{5 \cdot h^2} \\implies \lim_{h\rightarrow 0^+}\frac{e^h-1 -h}{5h^2}$

is this step legal

[solid cobalt]

But it is not 0/0 for some reason 🤔

Ok let me see

Yes of course it is

But is it helpful?

Try to join everything in a single fraction

Yes

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[solid cobalt]

Yes

Now l'hopital if you want

[gentle zephyr]

still 0/0 I think

[solid cobalt]

L'hopital makes that anoying -1 go away

And solves 0/0

(e^h-1)/10h

[gentle zephyr]

$\lim_{h\rightarrow 0^+}\frac{e^h-1}{5h \cdot h}-\frac{1}{5 \cdot h} \\implies \lim_{h\rightarrow 0^+}\frac{e^h-1}{5h \cdot h}-\frac{h}{5 \cdot h^2} \\implies \lim_{h\rightarrow 0^+}\frac{e^h-1 -h}{5h^2} \\implies \lim_{h\rightarrow 0^+}\frac{e^h -1}{10h} \\implies \lim_{h\rightarrow 0^+}\frac{e^h}{10}$

[solid cobalt]

So it is still 0/0

No

You didn't l'hopitalised well

[gentle zephyr]

,w differentiate e^x

[soft zealot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by __melomaniac

[solid cobalt]

Bro, the derivative of h is 1

[gentle zephyr]

you are right and i am stupid

[solid cobalt]

Nope, the derivative of 1 is 0

[gentle zephyr]

fuckkkkkkkkkk

[solid cobalt]

Try again

[gentle zephyr]

still we need to lhopi

again

[solid cobalt]

Yes you can do l'hopital

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[solid cobalt]

So what is the right derivative?

[gentle zephyr]

1/10 finally

lets do left derivate now using definition

eine moment bitte

$\lim_{h\rightarrow 0^-}\frac{\frac{1}{10}\left(2+h-2\right) + \frac{1}{5}-\frac{1}{5}}{h} \\implies \lim_{h\rightarrow 0^-}\frac{\frac{1}{10}\left(h\right) }{h} = \frac{1}{10}$

[solid cobalt]

No

You mixed x and h

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[solid cobalt]

Yes it seems right

Is it derivable at x0=2?

[gentle zephyr]

it is

[solid cobalt]

Goof

Good

[gentle zephyr]

when we took the limit of the incremental coeff, both cases of the piecewise gave the same derivative when x0 = 2 I think either from left and right

[solid cobalt]

Yes

[gentle zephyr]

I usually analyze continuity and differentiability when I asked if f(x0) is differentiable}

but here the question was another thing I guess

also very complicated

dunno why that incremental coefficient aswell as the f(x+h) was lowkey hard to see

thank you for the help

[solid cobalt]

Professors usually teach to check continuity always

If the function is not continuous it can't be differentiable

Some teachers also think that checking continuity is something kind of compulsory that must be done

But it is not the case you can go with differentiability and if the function is continuous you'll see it is not differentiablr

[gentle zephyr]

yeah maybe we killed two birds with one shot by checking differentiability right away

thank you for the help, god bless you category

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[hexed kiln]

Could someone help me with this?

[final tangle]

what have you tried

[final saddle]

@hexed kiln Has your question been resolved?

[hexed kiln]

Just completely stuck

I have brain fog atm + I’ve done 45 other questions

<@&286206848099549185>

[steep ruin]

Hello

I will help

[hexed kiln]

Please do

I’ve done 45 questions and am contemplating everything

I need help finding the highest common factor of 28acd and 36cb

[lucid pulsar]

well first look at what parts of 28acd appear in 36cb

[hexed kiln]

It would be 4 right?

[lucid pulsar]

okay and what else

[hexed kiln]

For 28 it’s 4 and 7 and for 36 it’s 4 and 9

[lucid pulsar]

yes 4 is one part of it, what do you think you need to look for now

[hexed kiln]

I’m not sure

[lucid pulsar]

what about the letters?

[hexed kiln]

C is the only one that appears twice

So itd be 4c

[lucid pulsar]

yes

[hexed kiln]

But that only gives me one set for the co ordinates

Wait I only need one

Sorry!

[lucid pulsar]

no worries!

[hexed kiln]

My brains a little tired!

Thanks!

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[zealous lava]

Explain why Pr(A)=0.3,Pr(B)=0.5, and Pr(A∩B)=0.4 represent impossible events.

[solid cobalt]

Don't you have a context?

What have you tried?

Do you understand the meaning of

$$A\cap B$$

[soft zealot]

Categorist

[zealous lava]

just want confirmation -- is this correct --** Pr(A) = 0.3, Pr(B) = 0.5, and Pr(A∩B) = 0.4 represent impossible events because the probability of both A and B happening together exceeds the probability of either A or B occurring individually, violating the fundamental rules of probability.**

@solid cobalt

[quaint cosmos]

yes

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[feral cobalt]

If the distance between two points is sqrt ((x2-x1)^2+(y2-y1)^2)
Then, in vectors, when you have two points: say, A(2, 6) and B(1, 3), what exactly is the vector AB(-1, -4) ?

[feral cobalt]

that's B-A

[barren hound]

the vector AB is the vector that describes the straight line displacement from A to B

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[hidden kiln]

Can someone pls help me to understand the Sine and Cosine graphs with different periods?

[hidden kiln]

Like idk how to plot the graph y = cos (1/4) x

!status

[final saddle]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[hidden kiln]

1

[barren hound]

,tex .transformation rules

[soft zealot]

hayley

[final saddle]

@hidden kiln Has your question been resolved?

[hidden kiln]

I still don’t get it

And btw 0<=x<=360

[final saddle]

@hidden kiln Has your question been resolved?

[hidden kiln]

<@&286206848099549185>

[feral robin]

At x=0x=0:
y=cos⁡(1/4×0)=cos⁡(0)=1

At x=90x=90:
y=cos⁡(1/4×90)=cos⁡(22.5∘)≈0.9239

At x=180x=180:
y=cos⁡(1/4×180)=cos⁡(45∘)=2√'2≈0.7071

At x=270x=270:
y=cos⁡(1/4×270)=cos⁡(67.5∘)≈0.3827

At x=360x=360:
y=cos⁡(1/4×360)=cos⁡(90∘)=0

[final saddle]

@hidden kiln Has your question been resolved?

[hidden kiln]

How do u know what cos of 22.5 is??

Idk that

And I think this question is meant to be non calc

Calculator

And I don’t think you can use that formula too

Cuz I’ve not been taught that formula yet

This question is from a textbook btw

Oh

But is there any other way to do it

I think it’s a better idea to send pics of what my textbook taught me

Wait a sec

Wait I’ll send

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[hidden kiln]

.reopen

[final saddle]

✅

[hidden kiln]

I need to graph y=cos(1/4)x using this knowledge

@tranquil pine

<@&286206848099549185>

[final saddle]

@hidden kiln Has your question been resolved?

[hidden kiln]

<@&286206848099549185>

[final saddle]

@hidden kiln Has your question been resolved?

[hidden kiln]

Can someone please help me

[final saddle]

@hidden kiln Has your question been resolved?

[near fulcrum]

change the period from over 2pi to over 1/4

so the entire sinusoid has to hit over 1/4

amplitude doesnt change only period

very messy but hope it makes sense

except change to a cosine graph

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[chilly beacon]

i don’t understand why at thoose points they are 0?

[wild grotto]

What do you expect them to be?

[chilly beacon]

like when they are at min or max that means they are at 0?

[clear moon]

the graph on the right is the slope of the curve on the left

notice that at those local min/max points, your curve on the left “turns around” to create a peak or valley

if you imagine how the slope is changing, let’s say when you’re approaching a minimum, then as you approach the minimum from the left you’d be decreasing so your slope would be negative, then you’d hit your minimum, then you’d be increasing as you move right from the minimum so your slope would be positive

that must mean that at the minimum, the slope is 0

you can also see this visually, you can think about your slope at a point on the curve on the left and notice that the curve looks almost “horizontal” at those min/max, which corresponds to the value of 0 on the right

[chilly beacon]

ong

tysm

fr

.close

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[hardy copper]

can someone help me with this sum: -3-4-...-51 ?

[hardy copper]

I've tried to resolve in the following way

-(3+4+...+51)

[vocal forge]

is this an arithmetic progression?

[hardy copper]

-(1+2+3+...51) - 3

I need to do a firework or something

we didn't study arithmetic progressions

we study it at highschools in my country

[vocal forge]

Can you tell the exact problem

[hardy copper]

I am in 8th grade

N = f(1) + f(2) +... + f(25), where f(x) = -2x-1

find n

oh f

[vocal forge]

You didn't learn AP?

[hardy copper]

I'm in middle school

I didn't not.

I just know about it cause I like math and I did some research

from ap to complex nrs and integrals

but I think I'm doing something wrong w this sum

[icy glacier]

What is f(2)?

[hardy copper]

:D

-5

[icy glacier]

So that’s the issue?

[hardy copper]

so the sum would be -3-5-7-....-51

oh

there is another problem

never worked on gauss with odd nrs

nevermind, thank you very much for helping me with f(2) 💀

I will pay more attention

have a great day !

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[mighty spade]

If a function is strict monoton Growing, does that mean its bijektiv?

[amber holly]

Depends on the codomain

Let f: R -> R be given by f(x) = x for x <= 0 and f(x) = x+1 for x > 0

f is strictly growing, but not bijective

[clear moon]

you can guarantee injectivity but not surjectivity, as mentioned before the surjectivity depends on the codomain defined

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[full halo]

What did i do wrong?

[agile coral]

Full question?

[full halo]

The log>0

[agile coral]

Cube root of x is positive when x is positive

[full halo]

I dont get it wym

[vocal forge]

Do we need to find the domain?

[full halo]

Need to find when >=0

[agile coral]

Where did you get the x>1 from?

[full halo]

The x^1/3>1

[agile coral]

Oh wait nvm

Gimme a sec

[full halo]

Bro u ok?

[agile coral]

Sorry, got caught up in a different channel

[full halo]

Oh

[agile coral]

Mb

[full halo]

Dw

[agile coral]

The 1/3 checks out
There's definitely a problem with the 1 though

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[full halo]

Wym

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@full halo Has your question been resolved?

[full halo]

<@&286206848099549185>

.close

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[normal juniper]

can someone please help me with question c

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[candid jasper]

prove that

[candid jasper]

please guys!

<@&286206848099549185>

i need helpp

please help me

[tranquil pine]

Write it's as cos/sin

[candid jasper]

i did that

it doesnt wprk

worjk

[tranquil pine]

Use area formula

S=Δ = (1/2) * b * c * sin(alpha).

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[ancient pulsar]

hello

[ancient pulsar]

how do i prove part D

help is appretiated

[tranquil pine]

is this your test ?

[ancient pulsar]

my friend's test

[tranquil pine]

tell him to do it yourself, we usually dont answer test questions

[ancient pulsar]

this test was a year ago-

i am just tryna figure the solutions

[tranquil pine]

oh may bad, sorry

[ancient pulsar]

;p

[violet totem]

So have you figured out all the questions (a,b,c)?

[ancient pulsar]

part a nope

[violet totem]

why do you want to solve question d first then?

[ancient pulsar]

cuz i gave up on A xD

[violet totem]

And is there more information on the paper about this exercise?

[ancient pulsar]

nope thats all the given

[violet totem]

The notation for question a confuses me

have you learned what a 'normal vector' is yet?

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[tranquil pine]

im gonna sound hella dumb

[shell swallow]

how

[tranquil pine]

how do u work out relative frequency bro

[fast arrow]

Can you be more pacific with your question?

[shell swallow]

Idk what he mean too tb

[tranquil pine]

wait lemme take a photo

idk how to do this bru

and im doing a foundation exam on the 3rd

im dumb

[fast arrow]

To calculate relative frequency divide the number of occurrences with the total number of samples

[tranquil pine]

all without a calculator too bro om

im cooked

thanks bro anyway

.close

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[somber star]

.claim

is B a textbook error?

[somber star]

both me and a friend have no idea how to a. solve this or get farther than a second derivative which is apparentally wrong according to the answer

[timid sinew]

so you want to find the extrema

all you need to do is set the first derivative equal to 0

[somber star]

i meant B

SORRY

my brain paused

B makes 0 sense to me

[timid sinew]

why doesn't b make sense?

they just set the derivative of x - 2sqrt(x) equal to 0

thats just 1 - 1/sqrt(x) = 0

simplifies to sqrt(x) = 1

only possible answer in this case is x = 1

then they plugged x = 1 back into the original function to get when x = 1, y = -1

so the pint (1,-1) is a critical point

then yeah take the second derivative and plug in x = 1 to determine concavity

so the second derivative is $\frac{1}{2} \frac{1}{\sqrt{x^3}}$

[soft zealot]

Potatomonke

[timid sinew]

plug in 1 you get 1/2

since f''(x) > 0, you know the point is concave upwards and is a minimum

[lavish flume]

Bro huh

That 100% doesn’t make sense

That’s sum from other space

[timid sinew]

well

tbh they did say confirm your answers graphically

so you couldve just graphed it

[lavish flume]

Ye we don’t take that

What grade is that

.

[timid sinew]

its regular calc

derivatives and concavity

[lavish flume]

Ye no

I’m still in trapezoid

Leave me be

[timid sinew]

ohh

riemann sums?

[lavish flume]

HUH

[timid sinew]

geometry?

[lavish flume]

ye

[timid sinew]

ohhhh

[lavish flume]

Im grade 8

[timid sinew]

then why did u start talking about derivatives 💀 I thought this was for calc when u said that

[lavish flume]

Can u please explain

Wtf

Is

[timid sinew]

yeah I think all they wanted was for u to look at the graph

[lavish flume]

Derivates

?

[somber star]

this is calc

[lavish flume]

Wtf is that

[timid sinew]

yeah ik but then bro said he was in geometry

so idk why he was even talking abt them in the first place

thats why I explained it using derivatives

[lavish flume]

…

[timid sinew]

I think they legitimately just want you to graph it

and look for minimums and maximums

[timid sinew]

WAIT

OMG I GOT SO CONFUSED

i thought this was angy's channel for a sec 💀

[somber star]

oh

wow

dude

when i saw that

my brain just exploded and i didnt see

that i could solve for

sqrt x=1

[timid sinew]

lol

np

sorry for the confusion

i forgot this was ur channel for a sec

[somber star]

hahah

[timid sinew]

i thought it was angy 💀

[lavish flume]

Bro

1 I’m not a dude💀

2 I’m a whole diff person

[somber star]

lol

[lavish flume]

3 I WAS ASKING WTF IS THAT

[timid sinew]

sorry u confused me when u jumped in out of nowhere

[lavish flume]

ye mb

[timid sinew]

np

[lavish flume]

I saw u typing non human shit

[timid sinew]

if u think thats non human go check some of the other channels

@somber star u good now?

[somber star]

i tried to figure out

how

1-1/sqrt x =0

goes to

sqrt x = 1

but

my calculator isnt giving same answer

neither is symbolab

im so confused rn

[timid sinew]

dont use a calculator

u just manipulate the equation algebraically

so move 1/sqrt(x) to the other side

becomes 1 = 1/sqrt(x)

then multiply both sides by sqrt(x)

u get sqrt(x) = 1

[lavish flume]

BRO THE PROBLEM IS THAT IM FAILING WHEN I ONLY TAKE BASIC THINGS AS EQUATIONS TRAPEZOID MIDSEGMENT THEOREM OR PYTHAGOREAN THEOREN

SO IDK WHTA U TALKING ABT

[somber star]

oh

man i am

[timid sinew]

ur in 8th its fine

[lavish flume]

Sigh idk wtf she be saying in class

Math isn’t for humans in my head

[timid sinew]

i slept thru geo thats all i remember

[lavish flume]

Okay how are u here helping him

What did u do

[somber star]

thanks for the help potato

[timid sinew]

np

[lavish flume]

Plus

From when did math have graphs

Tf is it biology

[timid sinew]

...

u prob took alg 1 alr right

there r graphs in that

and pre alg

[lavish flume]

No

Huh

What u saying

…

Listen

We took

Algebraic expressions

Factorization

Equation

Scientific notation

And

Uh when u have x in the denominator and u have to get the Domain of definition

Ye I actually have a question

[timid sinew]

wat

[lavish flume]

So

They asked

To factorize p(x)

I did

Then they asked to get p(x)=0

I also did

They then asked

To reduce and expand p(x)

Now to do that

Should I take

The factorized form

Or the original form

[timid sinew]

original?

[lavish flume]

How tho

[timid sinew]

it kind of depends on the problem

[lavish flume]

Wait

Imma send it

In exercise 3

Ye btw idk any of that cause tahts not my homework nor paper I just took it to like uhm get better in solving

Like extra shit

[timid sinew]

so you dont know any of this?

[lavish flume]

I do

I solved all

The upper shit

But got stuck in

Exercise 3

Since it’s been a long time

That I like solved shit with

Domain and reduce

And factorize

Tho I didn’t find difficulty in factorization

I have my exam in June 12 my final and I understand what were taking but I forget too fast

And I don’t review so like

It’s sum new to my brain everytime

[final saddle]

@somber star Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

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Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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 coral]

help

[tranquil pine]

is

o

so

[pseudo coral]

what

help me please

[tranquil pine]

what is this in

[pseudo coral]

Algebra 2

[tranquil pine]

ok

[pseudo coral]

pretty fire

[timid sinew]

what do you need help with

[pseudo coral]

Two helpers

is kinda fire

uh

[timid sinew]

like what part of it specifically

[pseudo coral]

like all ofi t

[timid sinew]

you know what a midline is right

[pseudo coral]

alright im not that dumb

midlines 45.17 right

[timid sinew]

mhm

[pseudo coral]

is it in seconds or cm

[timid sinew]

...

[pseudo coral]

im lazy

dont

dont do this to me

[timid sinew]

read the question

[pseudo coral]

ive been up since

yeah its cm trust

[timid sinew]

cm

seconds is the input

cm is the output

[pseudo coral]

is it a b c d

[timid sinew]

think about what the midline means

its the "middle" of the values

or another word for that

[pseudo coral]

averg

i got it right

fire

[timid sinew]

at least try the deltamath urself before sending it 💀

[pseudo coral]

this guy found out my strat

yeah i know how to do the majority

i need help on the next thing though

[timid sinew]

ok

[pseudo coral]

is 2pi/9

its the period

[timid sinew]

the period is 2pi / (2pi/9)

[pseudo coral]

right

yeah yeah

[timid sinew]

so its 9

[pseudo coral]

yeah

cm

[timid sinew]

no

[timid sinew]

in this case the period is the amount of time

before the values start to repeat

[pseudo coral]

so d?

[timid sinew]

so its seconds not cm

[timid sinew]

yeah

[pseudo coral]

alr

we got some more

to do

[timid sinew]

try it urself first

we aren't here to just give you answers 💀

[pseudo coral]

hey hey

lets

think about this

can you atleast help me

looking at it

so whats the format for this

igts co

cos

a
b
c
d

[timid sinew]

y = a cos( b( x - c )) + d

[pseudo coral]

y=acos(b(x-c)) + d

yeah that

y = 120 cos (b(x)+712

right

is that right

potato

monke

@timid sinew

this guy died

@tranquil pine

yeah ill just close thsi then.

.close

[final saddle]

Channel closed

Closed by @pseudo coral

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[gentle zephyr]

let $a_n = \frac{6^n \left(n+1\right)^n}{5^n \cdot n!} + 3\\$ and let $f: \mathbb{R} \to \mathbb{R}$ be a function such that 1 $\leq$ f(x) $\leq$ 4 $\forall x \in \mathbb{R}.\\$ Consider $b_n = \frac{f(a_n)}{a_n} + 2\\$ find $\lim_{n \to \infty} b_n$

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[ocean stratus]

!status

[final saddle]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[gentle zephyr]

1

[feral ginkgo]

have you figured out what's the limit of a_n?

[gentle zephyr]

its diverging to +inf

[feral ginkgo]

yh I think that's right

[gentle zephyr]

I applied d'alembert criterion but I am lowkey fucked, dunno how to continue

[feral ginkgo]

you're told that f(x) is between 1 and 4

for all x

so $\frac{1}{a_n}+2 \le b_n \le \frac{4}{a_n}+2$

[soft zealot]

lgkoo

[gentle zephyr]

I dont get it

[feral ginkgo]

a_n is just a real number

for any fixed n

so 1 <= f(a_n) <= 4

[gentle zephyr]

I get it now

[feral ginkgo]

k, now can you figure out the last step?

[gentle zephyr]

no

I need more handholding

[feral ginkgo]

hint: Pinching/squeezing thm

[gentle zephyr]

what about it

we know by squeeze theo that if both sides of the inequality is same limit is that

[feral ginkgo]

yh

[gentle zephyr]

here it isnyt

[feral ginkgo]

why

[gentle zephyr]

ok

lim bn is 2 then?

[feral ginkgo]

yeah

and you understand why?

[gentle zephyr]

you asked me at the start if I knew that an diverges to +inf

I nodded

[feral ginkgo]

yeah, that's the key.

[gentle zephyr]

low key why though

[feral ginkgo]

oh

I thought you got it

well a_n tends to infinity

so 1/a_n tends to zero

then both sides tend to 2, thus by Pinching thm b_n tends to 2

[gentle zephyr]

what is this f(ax) crap

[feral ginkgo]

ax?

you're told that f(x) is between 1 and 4

for** all** real numbers

and a_n is just a real number

no matter what n you pick, no matter how large n is, f(a_n) is still between 1 and 4

[gentle zephyr]

so basically its bounded

[feral ginkgo]

yes

[gentle zephyr]

f(an)

is bounded

[feral ginkgo]

yes

[gentle zephyr]

ok I got it

lowkey hard though

closing, xoxo

big thanks

.close

[final saddle]

Channel closed

Closed by @gentle zephyr

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[full halo]

to solve i thought about considering the log as 1+x with the x being 0

because n/n+1=1

and 1/n+1=0

so i put that as asymptote to n/n+2

but is wrong

why?

[solar glade]

Rewrite this as log((n+1)/(n+2))/(1/n) and use lhopital

[feral ginkgo]

out of curiosity, can you use l'hopital if n is integer?

[solar glade]

Sry i think i am not understanding the question

[fast arrow]

Then the answer is no, lol

[solar glade]

U say u cannot use lhopital here?

[full halo]

uhm

so uhhh

[fast arrow]

Are you familiar with log limits?

[solar glade]

Because i just did and i got it

[full halo]

wym like lim0 logx=-inf?

[feral ginkgo]

I was just wondering if the fraction is in terms of n, and if n is integer, then can you still use l'hopital? Cuz typically for l'hopital it is in terms of x where x is real numbers

[full halo]

hopital is when 0/0 of inf/inf

[solar glade]

This is 0/0

If u rewrite as i said

[feral ginkgo]

but the part where you take derivative

of numerator and denominator

[full halo]

yeye i get it i can use hopital but what was wrong from my logic?

[feral ginkgo]

doesn't that require them to be functions of real numbers?

[solar glade]

I might have overlooked something but where does it says n is integer

[full halo]

n is inf

samuel do u spot some error in my logic i said earlier?

[feral ginkgo]

oh no it didn't specify that n is integer, so n could very well just be real here. But seeing n just makes me wonder what if n is integer lol. It's not specifically for this question, more just a genuine question that I have.

[solar glade]

Oh ok, miss understand

By me

[full halo]

samuelll

[solar glade]

Relax lol

I dont even understand your logic

Im reading again

[full halo]

log (1+(1/x)) asymptote to 1/x

here we have log((n+1/n+2))

[solar glade]

Yes but how do u continue from there

[full halo]

= log (n/n+2)+(1/n+2)

n is inf so = log(1+(1/n+2))

this last part is 0 just like 1/n

so this log is asymptote to 1/n+2

[solar glade]

To which direction

[full halo]

wdyjm

[solar glade]

How is that true?

I want your explanation

[full halo]

bro i gave wym

@solar glade

[solar glade]

So u made the limit when n->inf like nlog(1+1/n)?

[full halo]

yes

[solar glade]

What is wrong i think

Let me check

[full halo]

log(1+1/n+2)

[solar glade]

Ok so

1+1/n is bigger than 1 right?

[full halo]

mh?

[solar glade]

And (n+1)/(n+2) is smaller than 1

So one is negative and the other positive

When u make the change

U altere the limit

Dont know even if altere is a word in english

Do you understand what im talking about?

So your changed limit will give 1

While the original -1

[full halo]

n+1/n+2 is 1

[solar glade]

When the sign changes is not the same

And here inside the log

The sign changes

[solar glade]

This is not true

The limit approaches to 1

[full halo]

uhmm

[solar glade]

But one will be 1.0000000…1

The other 0.999999…

[full halo]

how u know ?

[solar glade]

Because n+2>n+1

Which. Makes the division <1

While 1+1/n is > 1

[full halo]

mhh

k

[solar glade]

Does this make sense to you?

[full halo]

ye

is there another way without hpotial?

[solar glade]

Yes u can

Use e^ln of that

[full halo]

log?

of log?

[solar glade]

Lim x->inf e^ln(xln((x+1)/(x+2))

[full halo]

but is x->inf

[solar glade]

n instead of x hut whatever

Is the same

Yeah sry typo

And now i can aply log power rule

And rewrite as

e^(lim x->inf ln(x ln ((x+1)/(x+2)))

[full halo]

but how does this solve

<@&286206848099549185>

[final saddle]

@full halo Has your question been resolved?

[final saddle]

@full halo Has your question been resolved?

[final saddle]

@full halo Has your question been resolved?

[solar glade]

@full halo $x \ln\left(\frac{x+1}{x+2}\right) = \ln\left(\left(\frac{x+1}{x+2}\right)^x\right)$

[soft zealot]

Samuel

[solar glade]

$\frac{x+1}{x+2} \approx 1 - \frac{1}{x}$

[soft zealot]

Samuel

[full halo]

And what?

[solar glade]

Ln of that is aprox that

So when u get

(1-1/x)^x

U know the limit is 1/e

Now do the ln(1/e)

And u get the solution

[full halo]

Ok thx

Btw how did u get it with hopital

Cuz I did hopital but i got a complex stuff

[solar glade]

What derivative u got in the numerator

[solar glade]

that looks fine

If u multiply

U get 1 for the first term

And…

The second one of the x+2 goes to the denom

[full halo]

The whole thing becomes -(x²/(x+1)(x+2))

[solar glade]

U mean after derivating the 1/x?

Ok so now

[full halo]

Y

[solar glade]

FOIL denom

[full halo]

Foil?

[solar glade]

And divide numerator and denominator by x^2

Expand

-x^2/(x^2+3x+2)

Now u just divide numband denom by x^2

And u get -1 in the numerator

And 1 in the denominator

[full halo]

Thx bro

[solar glade]

Cause 3x/x^2 is 0

[full halo]

Were these the only 2 solution?

I feel like they wanted me to find a quick easy way

[solar glade]

The easy way is lhopital

The fast way is the other

With 1/e

Although both are kind of fast

I dont recall right now another way

[full halo]

How u figure this?

[solar glade]

Taylor series

[full halo]

Uhm which?

Log(1+x)?

[solar glade]

https://en.m.wikipedia.org/wiki/Binomial_approximation

[final saddle]

@full halo Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

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[final saddle]

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.

[proven solstice]

Hi im having trouble with q 14

[proven solstice]

This is where in up to atm

is there a way to make p equal smth?

[agile coral]

Nah
I think you're just done

[proven solstice]

I have realised i made a huge mistake

Can someone check if this is ok for me?

[tranquil pine]

yeah it's correct

[proven solstice]

Thankss

.close

[final saddle]

Channel closed

Closed by @proven solstice

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[final saddle]

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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.

[tardy sigil]

write cot as cos/sin

cos * cos^-1 = 1

sin^-1 = 1/sin

sin will come in denom

you can solve the fractions

[viral marten]

But it will be complicated

[tardy sigil]

no

its very simple

[viral marten]

I solved it and it is coming as tan(2arcsin(lsinxl+lcosxl)

[tardy sigil]

Oh i missed smthing

my working is wrong

ignore that

srry i gtg

[viral marten]

Yes you missed mod

[tardy sigil]

well what I did is blunder and crime srry

[viral marten]

Yes crime

[tardy sigil]

if sm1 doesnt help in 15 mins ping helper role

i gtg sorry

[viral marten]

Ok

<@&286206848099549185>

[silent cove]

@viral marten take cot as cos/sin and cos^-1 as 1/cos.

as cos get cancelled and left part becomes cosec(|sinx| + |cosx|)

right has a sin^-1 which is also cosec

take the - sign outside from the brackets and the right part becomes = -cosec(|sinx| + |cosx|)

take the (|sinx| + |cosx|) common

you have (|sinx| + |cosx|)(cosec - cosec)

solve this and you have the answer

[final saddle]

@viral marten Has your question been resolved?

[final saddle]

Channel closed

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[viral marten]

Bro are you dumb

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[silent cove]

correct me garvit. i'm sorry if i wrote something wrong

[viral marten]

What grade are you studying in

[silent cove]

what is the error?

[viral marten]

First tell me that

[silent cove]

no need

[viral marten]

Sin^-1 is a function bro

It's not 1/cosec

[blissful condor]

you don’t need to be so harsh

[viral marten]

It's a 12th grade question

[viral marten]

Sorry

[silent cove]

you mean this one?
theta = cos-1( something something)

?

[viral marten]

Yes

[silent cove]

oh alr. my bad

i took it for the power

[viral marten]

Sorry to be harsh but it's a mathematical crime

[silent cove]

they look exceptionally similar, but i am sorry for that

[viral marten]

It's a crime

😁

[silent cove]

that's one way to put it correctly

i think i have messed up the help system because it took my "correct me" as a question.

should I close it?

[viral marten]

Ya

[silent cove]

alr

[viral marten]

Next time aware of this blunder

[silent cove]

thnx for correcting me. next time i need to ask it first

[silent cove]

sure

thnx

[viral marten]

It's never in the power

Never ever take it as a power

[silent cove]

what about if it is -2?

would that be considered 1/sin^2? or sqr of the same function?

[viral marten]

If it is on the power it will be (cosx)^-2 not cos^-2x

[cedar ore]

i feel like i need to point out that @silent cove uses emacs

so deal with caution

[silent cove]

i do

[cedar ore]

use nvim

[silent cove]

i use it too

[viral marten]

If you are not in 12th grade you will come to know about it more in 12th

[cedar ore]

delete emacs

[silent cove]

no it is faster

[cedar ore]

no

[silent cove]

i can even open books in it

[cedar ore]

emacs binds suck

[silent cove]

pdfs and epubs

[silent cove]

god-mode

[viral marten]

Ok @silent cove

[cedar ore]

why r u using emacs if you use vim binds

LOL

[silent cove]

alr this is getting out of way

[silent cove]

i don't use vim-binds. i use god-mode

.close

[final saddle]

Channel closed

Closed by @silent cove

Use .reopen if this was a mistake.

[cedar ore]

it's practically vim

[silent cove]

no it is not

you don't use x+c to exit vim do you?

[blissful condor]

:wqa

[final saddle]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[hoary cairn]

how is this 6!

[rugged scaffold]

for the first person to sit there are 6 seats, for the 2nd person there are 5 seats and so on

so the number of ways = 6x5x4x3x2

which is basically equal to 6!

[hoary cairn]

okay so if it was 7 seats

what happens then

[rugged scaffold]

if it is 7 seats and 5 person then it would be 7x6x5x4x3

[hoary cairn]

okay

if the question was worded differently

would iit have been 5!

[rugged scaffold]

it depends on what the question is asking for

[hoary cairn]

Cus what i was thinking

how can 5P6

be possible

[rugged scaffold]

yeah its not possible

[hoary cairn]

okay thanks

.close

[final saddle]

Channel closed

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[tranquil pine]

how is cot^2x = cosec^2x - 1

[tranquil pine]

do we just know this or is it somehow derived

because cot^2x = 1/tan^2x

[silver marlin]

well you start with sin^2x + cos^2x = 1

then divide by sin^2x

which becomes 1 + cos^2x/sin^2x = 1/sin^2x

and since cos^2x/sin^2x is cot^2x

and 1/sin^2x is csc^2x

[tranquil pine]

pack your bags and leave the office

.close

[final saddle]

Channel closed

Closed by @rough kettle

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[final saddle]

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[tranquil pine]

stupid question, but how do you solve x(x+c) = a(a+c)

[tranquil pine]

I know how to solve it but can you straight away say x = a and x = -a-c

through equating stuffs

[trail mango]

x(x+c) - a(a+c) has at most 2 real roots since it is a degree 2 polynomial

so if you find them

then you’re done

no matter how you found them

as for “how to solve” you can solve it like you would any quadratic equation

x(x+c) - a(a+c) = x^2 + cx -a(a+c) = 0

quadratic formula or factoring or whatever method you want

[tranquil pine]

Yes, I used the quadratic equation to do it

But i've seen people instantly giving me those answers lol

They're equating stuffs i guess or something

they're not supposed to do that

(x-5)(x-6) = (1/24)(1 + 1/24) and they instantly give me the answers that (x-6)= 1/24 or x-6 = -(1 + 1/24)

surely they aren't doing quadratic formula in 0.1 second right

[trail mango]

inspection is a perfectly valid way to find things

[tranquil pine]

no but there's a pattern isn't there?

(x-6) = first term and (x-6) = - (second term)

[tranquil pine]

same thing here

x = a or x = -(a + c)

[grim nebula]

the pattern is you stare at the factorisation (1/24)(1 + 1/24) and it becomes blatantly obvious that it is a factorisation with factors that differ by 1

which is precisely the requirement of (x - 5)(x - 6) = (1/24)(1 + 1/24)

if (1/24)(1 + 1/24) is a factorisation, then so is (-1/24)(-1 - 1/24)

[tranquil pine]

okay yeah interesting, i guess that holds for x(x+c) = a(a+c) as well right?

it differs by "c"

[grim nebula]

i mean

for that one if you dont immediately see x = a idk what kind of eyesight you have

[tranquil pine]