help-0

[cyan rapids]

Since that should make the fraction positive?

[ornate condor]

v/c would be

1 right

[cyan rapids]

If we want the sqrt function to work yeah

[ornate condor]

nono

when

this happens

v/c is

1

right

[cyan rapids]

I guess it's right since you keep saying it but I don't understand why

[ornate condor]

ok but

we want

sqrt(1-v^2/c^2)

and

v2/c2

shld also be

1 right

and we are

subtracting

some >1 val

from 1

so we get a neg val

right

[cyan rapids]

Yeah if the value is less than 1 then it doesn't work

[ornate condor]

nonono

u

ok so

if we hv

just consider

sqrt(1-a)

[cyan rapids]

ok

[ornate condor]

where a<1

does this exist?

[cyan rapids]

No

[ornate condor]

ok

if we

take

a=0.5

ehat happens

[cyan rapids]

We get sqrt(.5)

[ornate condor]

abd

and

does that exist

[cyan rapids]

Yes

[ornate condor]

ye so

a<1

the thing will exist

if we take like

a=-10

what would we get?

[cyan rapids]

sqrt(11)

[ornate condor]

ye anw

u kinda

get my point

[cyan rapids]

Wait so a<1 exists

[ornate condor]

but now

[cyan rapids]

Gotcha

[ornate condor]

yes

now

repeat with

a=1

does that exist?

[cyan rapids]

Maybe? Not sure if sqrt(0) exists or not, pretty sure it does

I would think so

[ornate condor]

it rxists

exists

now

with a>1

[cyan rapids]

It no longer exists

[ornate condor]

yayy

so

now back to the lim Q

[cyan rapids]

Q?

[ornate condor]

u kinda get what i was tryna say earlier

question

Q

[cyan rapids]

Gotcha

[ornate condor]

or not rly

[cyan rapids]

Let me go back and read it lol

[ornate condor]

lol

okie

just note the a earlier is like

v^2/c^2

[cyan rapids]

Yeah got that

So v^2/c^2 has to be less than 1

[ornate condor]

for the limit to exist

yepp

and

so

[cyan rapids]

Meaning that lim v->c+ L should approach -infinity?

[ornate condor]

thats why we take the

err

no

it

doesnt exist

so

thats how it was relavent

we

[cyan rapids]

I already tried putting in that it doesn't exist

[ornate condor]

take the

[cyan rapids]

Which was incorrect

[ornate condor]

nono

u put

[cyan rapids]

Wait but that would be for the right side

Not the left

[ornate condor]

yes

u chose dne for

[cyan rapids]

So the right side lim doesn't exist

[ornate condor]

v<c

aka

v approaches c-

[cyan rapids]

So the left side limit exists then

[ornate condor]

yeppp

[cyan rapids]

That's good to know

[ornate condor]

so

u got it now?

[cyan rapids]

Nope, lost from here

[ornate condor]

nuuu

[cyan rapids]

I at least know it exists

[ornate condor]

oki what r u lost with

[cyan rapids]

I usually plug in a number to see if something is a vertical asyntote or something but there's like no numbers to plug in

[ornate condor]

u can

just pick a number slighter larger or smaller

[cyan rapids]

Than 1?

[ornate condor]

doesnt always work but

works here

well

a val of v

greater or lesser than c

so u can try like

v as 1.1c

or

v as

0.9c

[cyan rapids]

So we are replacing v with values of c now?

[ornate condor]

i mean

i wouldnt do that haha

but

if u wanna try replacing values

u can try doing that

[cyan rapids]

Well I don't necessarily want to

[ornate condor]

to see which

ye so

just

know that

when we approach

[cyan rapids]

I'm just confused as to what I'm "trying" here

[ornate condor]

v->c+

[cyan rapids]

When we approach from the right, the limit doesn't exist

[ornate condor]

ok

then

when we go from the left

we know that

[cyan rapids]

Then the limit exists

[ornate condor]

yepppp

then

[cyan rapids]

But I have zero clue how to find what that limit is

[ornate condor]

what r y stuck on

ohh

um

so

we know that

v approaches c

so

considering the lim exists

v/c is 1

right

[cyan rapids]

Or less, yeah

[ornate condor]

ye

then

we just use

sqrt (1-1)

to get

0

!!!!!

[cyan rapids]

So the limit is just 0?

[ornate condor]

yepp!

[cyan rapids]

Hang on, so as long as v = c and either don't equal zero, this would work

[ornate condor]

hm?

[cyan rapids]

Nvm

[ornate condor]

no cuz

its

bot actually

not actually

0

its

like

slightly

positive

cuz

v/c

is a bit less than 1

[cyan rapids]

The computer is saying zero but ok

[ornate condor]

its like

lim v->c+ (v-c)

so

v is

approaching c

and is

slightly more than c

but we just

[cyan rapids]

And it can't approach if the values are the same

[ornate condor]

eval it into 0

[ornate condor]

wdym

[cyan rapids]

So zero is an estimation

I don't know

[ornate condor]

i

im sry idk what u mean again

[cyan rapids]

I don't know what I mean either if I'm being honest

But like

[ornate condor]

0 is like

the lim val

cuz

[cyan rapids]

If say both v and c are 1

[ornate condor]

v goes

[cyan rapids]

How could 1 approach 1

It's already there

[ornate condor]

arbitrarily close to c

[cyan rapids]

Gotcha on that part

[ornate condor]

wait no

its like

ok

lets

replace c with 1

v

[cyan rapids]

Ok

[ornate condor]

is still a var

i like x

[cyan rapids]

Ok

[ornate condor]

lets use x

so

weve

lim x->1

umm

of

[cyan rapids]

sqrt(1-x)?

[ornate condor]

lim x->1 (x+2)

[cyan rapids]

Or that

[ornate condor]

oh

that could work too

lol

[cyan rapids]

Limit is 3 there

[ornate condor]

yes

and

ok but

defn of limits is like

left and right limit has to agree right

[cyan rapids]

Yeah

Otherwise it doesn't exist

[ornate condor]

so for this

[ornate condor]

actually no

lets

[cyan rapids]

You plug in 1, get sqrt(0)

[ornate condor]

go back to this first

so

x+2

as x goes to 1

so

[cyan rapids]

It approaches 3

[ornate condor]

if we take it from the right side

x is

slightly kore than 1

right

[cyan rapids]

Yes

[ornate condor]

and from the left

x is slightly less than 1

[cyan rapids]

slightly less

[ornate condor]

ye

but

[cyan rapids]

Then averaging gives 3

[ornate condor]

the lim

nono

its no

averaging

its not

averaging

[cyan rapids]

ok

[ornate condor]

the

left lim

is exactly 3

the

right lim

is also exactly 3

lim is like

[cyan rapids]

So (3+3)/2

3

[ornate condor]

nono

we

do not average

wait

so

if we just consider

x -> 1+

of x+2

its saying

whats x+2

[cyan rapids]

3

[ornate condor]

as x goes

infinitely close to 1

from the right

so like

[cyan rapids]

It approaches 3, gotcha. So I would plug in a number close to one since I can't plug in 1

[ornate condor]

have u learnt epsilon delta

[cyan rapids]

I think?

[ornate condor]

omg u

shlda

[cyan rapids]

Those words are familiar

[ornate condor]

used that from the start

[cyan rapids]

Oh well

[ornate condor]

so like

[cyan rapids]

I got it though so that's good

[ornate condor]

given any epsilon

well

sure then

haha

ok but anw

for

sqrt(1-x)

as x->1

lim doesnt exist

cuz lim from 1 side doesnt exist

[cyan rapids]

Yeah

[ornate condor]

ye

i

think thats abt all

its been long

[cyan rapids]

Yeah I think I got it now

[ornate condor]

[cyan rapids]

Thanks for the help

[ornate condor]

yayy

❤️❤️

[cyan rapids]

.close

[ornate condor]

np

[lone heart]

Channel closed

Closed by @cyan rapids

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[lone heart]

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[opaque oyster]

How would you prove that 5^118 mod 9 = 4 in detailed text?

[opaque oyster]

gcd(5 , 9) = 1
φ(9)=φ(32)=32−31=6
Therefore by Euler’s theorem
56≡1(mod9)
⟹(56)19≡1(mod9)
⟹5114≡1(mod9)
⟹5118≡54(mod9)
⟹5118≡4(mod9)

I wish to improve upon this.

[lone heart]

@opaque oyster Has your question been resolved?

[opaque oyster]

.close

[lone heart]

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[alpine sable]

10xy + 0.25x2 + 100y2

[alpine sable]

i need to factorize it

and im struggling

we didnt even go over this stuff in class

[gilded vessel]

is x2 and y2 meant to be x^2 and y^2

$0.25x^2 + 10xy + 100y^2$

[ocean seal]

dog.

[wary stream]

$10xy + 0.25x^2 + 100y^2$?

[gilded vessel]

this?

[ocean seal]

dldh06

[gilded vessel]

have you heard of the perfect square formula @alpine sable ?

[alpine sable]

yeah

no

[gilded vessel]

it goes as follows

$(a+b)^2 = a^2 + 2ab + b^2$

[ocean seal]

dog.

[alpine sable]

ohh wait i have seen that

just havent called it by that name

[gilded vessel]

do you notice any similarity to the right hand side with your equation

[alpine sable]

only the last term, 100y^2 = b^2.

[gilded vessel]

organising the terms like this may help

[gilded vessel]

what about 0.25x^2

what would be the square root

[alpine sable]

0.25x^2 + 10xy + 100y^2

ohh

[alpine sable]

.5

[gilded vessel]

0.5x

but yes

and now try 2 * 0.5x * 10y

what do you get

[alpine sable]

2.5xy

[gilded vessel]

not quite

first of all what is 2 * 0.5x

[alpine sable]

ohh

x

[gilded vessel]

yeah sorry

$2 \cdot 0.5x \cdot 10y$

[ocean seal]

dog.

[gilded vessel]

here this

what do you get

[alpine sable]

yeah so 10xy

[gilded vessel]

works perfectly doesnt it?

[alpine sable]

yeah

[gilded vessel]

so can you see how you could factorise that now

[alpine sable]

(0.5x + some integer y)^2

[gilded vessel]

yep

remember that "some integer"

you have 100y^2 = ("some integer" times y)^2

[alpine sable]

so 10

10y

[gilded vessel]

yeah

remember we did this

[gilded vessel]

here

[alpine sable]

ohhh

[gilded vessel]

it needs to be 10y for the middle term to work as well

[alpine sable]

i get it now

thank you

[gilded vessel]

no problem

[alpine sable]

aight so

my homework gave me a really easy first question on that subject

and then they threw me a friggin monster of an equation

$\frac{1}{16}x^4 + 2x^2a + 16a^2$

[ocean seal]

InfiniteAxis

[gilded vessel]

hmm

this is actually just the perfect square formula again haha

except now with x^2

[warped light]

heres a hint: make a new variable t and say t=x^2

then substitute t and x

[alpine sable]

$\frac{1}{16}t^2 + 2ta + 16a^2$

oh crap

[ocean seal]

InfiniteAxis

[warped light]

exactly

[gilded vessel]

yepp

with practice you should be able to recognise such situations

[alpine sable]

so then (1/4t + some integer * a)^2

that some integer * 1/4t = 2ta

[alpine sable]

bet

[warped light]

its 2 * integer * 1/4t = 2ta

[gilded vessel]

remember its pretty easy to get this some integer by looking at the last term

[warped light]

a simpler way is to just square root the last coefficient tho

[gilded vessel]

$16a^2$ thus the integer is $\sqrt{16} = 4$

[ocean seal]

dog.

[gilded vessel]

what i do is take the square root of first and last coefficient and check if it works for the middle one

[alpine sable]

so the integer is simply 4a

[warped light]

yes

[alpine sable]

(1/4t + 4a)^2

[warped light]

now remember to substitute x back in

[warped light]

this

[alpine sable]

oh wait yeah

i got it

[gilded vessel]

also in the future when you are more accustomed to such equations you dont need to make any substitutions

keep in mind that t = x^2 is just for convenience

[alpine sable]

alright

[gilded vessel]

if you can recognise and solve while keeping it in the original form thats even better

[alpine sable]

okay

thank you

[gilded vessel]

further down the road there will be equations where substituting is still easier to do

[warped light]

(x^2+y)^2 = (x^2)^2+2(x^2)y+y^2

thats all it is

[gilded vessel]

but this one is rather trivial and for example in an exam situation would be a waste of time to make a whole new variable for substitution

[alpine sable]

.close

[lone heart]

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[stoic bough]

i do not understand

[slate jolt]

i assume "s" is how much he can spend

so in that case what can you tell about s?

[warped light]

if he spends 637 on his ticket how much does he have left?

[stoic bough]

1363

[warped light]

that means since he has 1363 dollars left, he can only spend less than or equal to that amount

[stoic bough]

so it would be the third option from the top

[warped light]

yes

[stoic bough]

oh ok thx

[warped light]

another way of looking at is to say that he has 2000 total dollars to spend, so the the cost of his plane ticket plus the cost of everything else cannot exceed 2000$

[stoic bough]

also i don’t understand this one

[warped light]

how much will you have left each week after spending 6.50 and saving 5.00?

[stoic bough]

3.50

[warped light]

can you figure it out from there?

[wary stream]

Is this a test or something?

[stoic bough]

it’s my homework

it’s a review from awhile ago that i don’t remember

[warped light]

you figured out that you have 3.50 left, so which inequality shows how much you are able to spend?

[stoic bough]

the 2nd one

[warped light]

not quite

[stoic bough]

wait no i meant the first

[warped light]

the second one says the amount you can spend is greater than or equal to 3.50, but you cant spend more than 3.50

[stoic bough]

i got the greater than or equal to signs mixed up

[warped light]

do you understand how to solve it now?

[stoic bough]

i think so

but there’s other ones i haven’t gotten to yet

so i’ll try them

[warped light]

just to summarize, you take the total money you have and subtract your fixed expenses

that will give you the amount of money you have left to spend which you can use to write an inequality

[stoic bough]

oh i get it now

thx

[warped light]

np, make sure to do .close if you don't need any more help so someone else can take this channel

[stoic bough]

ok i will after i’m done so i know if i need any more help or not

[warped light]

thats fine

[stoic bough]

i don’t know this one

@warped light

[warped light]

@stoic bough the number of cars is c, so c times the profit per car will give the total profit

and they want that profit to be greater than or equal to 300

[stoic bough]

so it’s the last one

[warped light]

yes

[stoic bough]

.close

[lone heart]

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[brazen berry]

Linear Algebra Question: Any advice to solve this? I can't remember how we covered the topic in lectures.

[lone heart]

@brazen berry Has your question been resolved?

[brazen berry]

<@&286206848099549185> sorry for the ping, dont want this thread to close aha

[brazen berry]

.close

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[abstract skiff]

Literal equation:

Ax - bc = xb - ac

[kindred anchor]

Looks good.

[ornate condor]

whats the Q lol or is that all

[lone heart]

@abstract skiff Has your question been resolved?

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[valid smelt]

is the greatest entropy a system with two possible outputs can have equal to 1 because a bit can encode two states

[valid smelt]

and then everything other than that 1/2 1/2 distribution would be less than 1

just need a sanity check kekw

.close

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[patent sluice]

is my solution here correct?

[patent sluice]

or is there a much better way solving this equation

[ornate condor]

,w solve (x+2)/(x-2) = x/(x+1)+2/(x-1)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Circle#0025

[ornate condor]

hm

something feels off

oh

yea u got that

u just gotta

put the

/6

over the whole thing

so 1/6

instead of 1+

[patent sluice]

ohh, okk thx

.close

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[ornate condor]

np

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[raven laurel]

Guys, I’m struggling with this question, any ideas please?

[ornate condor]

when did u join the project?

[raven laurel]

The question says since year 2

[ornate condor]

nono

[raven laurel]

Month 2 sorry

[ornate condor]

it say

yepp

then

[raven laurel]

Sorry lol

[ornate condor]

whats the

diff in rev b4 n aft u joined

b4 u joined is at 2m

n rn its at?

[raven laurel]

So the question is asking the difference between after I joined the project and b4 I joined th project? Sorry I’m afraid I didn’t get it correctly

[ornate condor]

um its

n b4 u joined

like

[fierce flame]

since the question asks for average monthly revenue, we have to find average of first two months(combined) and the last two months(combined) and find the difference between them

[ornate condor]

avg increase each month since u joined

said it wrong earlier

[fierce flame]

is my statement correct?

[ornate condor]

omg ive to include the first month as well

yes

i

misread

[ornate condor]

yes u are correct

[raven laurel]

So it should be (average revenue of m4 and m3) minus (average revenue of m1 and m2)

the answer should be £1445?

[ornate condor]

,w 1/2 * (6210 + 5950 - 4420 - 4760 )

[ocean seal]

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Requested by Circle#0025

[ornate condor]

1490

idk why that isnt loading on mine

but i got this

idk

if i entered a number wrong or u did

u can try checking again ig

[trim wagon]

yes i’m facing same issue today , discord bad

[ornate condor]

deep save me did i do it right

[trim wagon]

tl;dr

[raven laurel]

But the answer of 1490 isn’t exist in the answer list…

[ornate condor]

i

idk

i tried a few times but i

sorry

[raven laurel]

This is a tricky one ha, thanks for ur help btw

[trim wagon]

i’m sorry to interrupt but please screenshots!!

[raven laurel]

Ok wait

Sorry lol

[ornate condor]

@wanton tusk

how do

i cannot

:c

[raven laurel]

:c

[wanton tusk]

hi

:c

[ornate condor]

HIII

i got

[wanton tusk]

HII

👑

[ornate condor]

this

but

it isnt in the list

[wanton tusk]

mayb find the avg for first 2 mnths

[ornate condor]

👑

[wanton tusk]

then next 2 mth

[trim wagon]

hmm 🤔

[wanton tusk]

then -

idk HAHAHA

[ornate condor]

i used

[wanton tusk]

,w (4420+4760)/2

[ocean seal]

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Requested by swaggofishballs#1529

[ornate condor]

na

just

google it

wolfie

OMG

WOLFIE WORKED

[trim wagon]

,calc (4760+6120+5950)/3 -4420

[ocean seal]

Result:

1190

[ornate condor]

woah

[wanton tusk]

,w (6120+5950)/2

[ocean seal]

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Upgrade to WolframAlpha Pro!

Requested by swaggofishballs#1529

[ornate condor]

theres a calc func

[wanton tusk]

,w 6035-4590

[ocean seal]

Results provided by WolframAlpha

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

Requested by swaggofishballs#1529

[trim wagon]

ig thats ur answer sir

[ornate condor]

what did i do wrong T.T

OMG

WE

[trim wagon]

wut

[ornate condor]

ALL GOT DIFF ANSWERS

HAHHAHA

[trim wagon]

[ornate condor]

HAHHAHAHA

[wanton tusk]

HAHAHAHA

i got 1445

[ornate condor]

IMAGINE

4 diff answers

[wanton tusk]

but not credible

[ornate condor]

HAHHAAHA

[wanton tusk]

HAHAHA

[raven laurel]

Yeah and both of them in the answer list lol

[trim wagon]

what did fishballs do?

[ornate condor]

wait actually

[wanton tusk]

@trim wagon shd be right

[ornate condor]

its the most credible

the

op

also got that

anw

brb

❤️

[wanton tusk]

i don’t have helper role

HAHHA

[wanton tusk]

bye byeeee

[trim wagon]

neither do i

[wanton tusk]

WHAT IS THIS CRIME

don’t wry,, ure a helper at heart

[trim wagon]

but i’m confused here

[wanton tusk]

hmm

[trim wagon]

[wanton tusk]

@raven laurel are u allowed to do the qn twice

or only 1 attempt

[trim wagon]

nice idea lol

[ornate condor]

im\

bac

[raven laurel]

only 1. attempt lmao

[wanton tusk]

HAHAHA

[wanton tusk]

hihiii queen

[trim wagon]

im deep

[wanton tusk]

im swaggo

fishballs

[trim wagon]

wait but he joined at 2nd month

[ornate condor]

who

[wanton tusk]

ya

[wanton tusk]

@raven laurel

[trim wagon]

and avg of last 3 months is (4760+6120+5950)/3

[raven laurel]

yes

[trim wagon]

so idk but (4760+6120+5950)/3 -4420 seems logical no?

,w (4760+6120+5950)/3 -4420

[wanton tusk]

,w 6035-4590

[ocean seal]

Results provided by WolframAlpha

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

Requested by swaggofishballs#1529

Results provided by WolframAlpha

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

Requested by Deep.#0001

[wanton tusk]

ok there u go

[trim wagon]

what did you do swaggo

[wanton tusk]

use deep’s ans

[trim wagon]

no but why we getting diff ans

[wanton tusk]

I found avg for first 2 months and avg for last 2 months

[trim wagon]

ohh i c

thats not correct then

[wanton tusk]

since he joined after 2nd month

[trim wagon]

he joins on 2nd month

[wanton tusk]

oh

[ornate condor]

i

did the same

but got a diff

[wanton tusk]

see this is why I wear glasses

[ornate condor]

number

HAHAHA

[wanton tusk]

HAHAHAHA

i thought after 2nd month

oopsie

[trim wagon]

happens

[raven laurel]

So seems the 1190 is the answer? hahahaha

[wanton tusk]

ya ^^

[raven laurel]

ok thanks a lot guys

[trim wagon]

[raven laurel]

❤️

[wanton tusk]

🕊️

[ornate condor]

❤️

[trim wagon]

,tex \np

[wanton tusk]

,tex \np

[ocean seal]

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

[wanton tusk]

..

:c

[trim wagon]

.close someone

[raven laurel]

.close

[wanton tusk]

@ornate condor

[lone heart]

Channel closed

Closed by @raven laurel

Use .reopen if this was a mistake.

[ornate condor]

.close

[wanton tusk]

HAHAHHA

[ornate condor]

[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.

[worthy lily]

how did they get 5x/6

I am fine up to the point where it says Now Solving:

[serene junco]

You may find it more intuitive to say x=6u/5, rather than u=5x/6

The goal is to get the denominator into the form $\sqrt{36-36u^2}$ which can be simplified to $6\sqrt{1-u^2}$ so that you can do a trig substitution

[ocean seal]

tatpoj

[serene junco]

@worthy lily Does this help at all?

Go to an available channel up above. One of the ones that doesn't already have someone's name on it

[worthy lily]

it's -25x though

[serene junco]

I'm not sure what you mean. If you substitute $x=\frac{6u}{5}$, I think you'll find that the denominator becomes $\sqrt{36-36u^2}$, which can be simplified to $6\sqrt{1-u^2}$.

[ocean seal]

tatpoj

[worthy lily]

where is the x?

[serene junco]

We're substituting x = 6u/5.

x is 6u/5

[worthy lily]

sorry

this is really hard for me

[serene junco]

Once you make the substitution, the integral is in terms of u, not x.

That's okay

Have you done u-substitution before?

[worthy lily]

yes

but not like this

ok can we back up

[serene junco]

sure

[worthy lily]

the question starts at 5 / sqroot(36 - 25x^2) - 50x / sqroot(36 - 25x^2)

so I did u substitution

5 / sqroot(u) - 50x / sqroot(u)

du = -50x dx

so du / -50x = dx

or do I only sub one u?

not both

[serene junco]

Always both

[worthy lily]

ok

[serene junco]

If you make a substitution, you substitute for all the variables

[worthy lily]

so that would be 5/-50x sqroot(u) + 1 / sqroot(u) right?

we got rid of 50x on the one side

but it was added to the other side

am I going to have to solver for x and then put u into the x

[serene junco]

Okay hang on

I'm getting a little confused

[worthy lily]

I'm so bad at calculus

should I drop my class?

tonight is the last night

but it's held me back so long

[serene junco]

Lol wait dude you're asking a lot of questions lol

[worthy lily]

I want to try and defeat it

[serene junco]

In your class, have you been discussing trigonometric substitution?

[worthy lily]

yes

but I havnt been to class

I've been watching videos and doing hw

no point of me going to lecture when I don't know whats going on

[serene junco]

Hm

You're skipping class because you feel like you don't understand it?

[worthy lily]

maybe I should start though

yes

I just learned u substiution this week basically

[trim wagon]

well if you skip you won’t understand

[worthy lily]

they move so fast

[serene junco]

Yeah, skipping is just going to make it worse

[worthy lily]

it takes me time to learn it

[serene junco]

What is the last math class you took before this one?

[trim wagon]

then consult wit ur instructor

[worthy lily]

Calc 1 but it was like 7 years ago

[serene junco]

Ok

[worthy lily]

this is Calc 2 now

I'm ok on easier integrals

it's when they get complicated

I know what's going on

[trim wagon]

keep practising ig, but skipping class isn’t wise option

[worthy lily]

ok

I have 40 minutes to decide if I want to do this class or wait until next semester

[serene junco]

Okay

[worthy lily]

I was thinking do I study on my own for 3 months and show up in January

or just keep going?

[serene junco]

If you feel like you just got the hang of u-substitution, and your class is on trig substitution, then you are way behind

[worthy lily]

hahaha

but I dropped every class so this will be my only class

[trim wagon]

if you’re comfortable wit self studying then ig you can try

[worthy lily]

and I missed first 2 assignments

but they drop 2 lowest scores

so I havnt lost any marks yet

[serene junco]

No offence, but you're going to have more low scores if you're that far behind

[worthy lily]

I only have this class though

and I will put all my time towards it

[serene junco]

I don't mean to be rude, but you're not in a good position

[worthy lily]

all I need to remember is some trigonometric identities

I know like integral is of -sin is cos

so I'm starting to do trigonometric

and like sqroot(1 - x^2) is arcsin

1/sqroot(1 - x^2)

[serene junco]

Okay

[worthy lily]

should I drop

or just go for it

there's also a way I can do self paced online only

but I have to send letter to my university to ask for permission but they will accept

[serene junco]

I can't give you that advice. But this is technically enough to solve this problem

[worthy lily]

I was just thinking that the normal pace class would make me work hard

the thing is

I can't even get to that step

I don't know where the 5x / 6 came from

[quick laurel]

Regarding $5\int\frac{1}{\sqrt{36-25x^2}}dx -50\int\frac{x}{\sqrt{36-25x^2}}dx$ If you refer to a "common" integral table. You should find that these integrals align with provided reductions

[ocean seal]

Thasis

[worthy lily]

think if I come here every day and I only have 1 class

I could catch up?

sorry what do you mean Thasis

align with provided reductions

I did u substitution on the denominator right

50x / sqroot(u)

is that a good step?

then du = -50x dx

so du / -50x = dx

and we can cancel out the 50x on top

[quick laurel]

For Instance $\int\frac{1}{\sqrt{a^2 \pm x^2 }}dx = arcsin(\frac{x}{a})$

I would reason to say, that most professors will provide you with a table of commonly used integrations

that prevent you from having to do exactly what you're doing.

[ocean seal]

Thasis

[quick laurel]

edited

[worthy lily]

ohhh

[quick laurel]

Do you see how this could apply?

[worthy lily]

ok

so any time we see there is squared numbers

in that form

[quick laurel]

that's a fantastic indicator. A lot of integrations that have a similar form as the above, have some sort of equivalence that is well known.

So for the second portion;

[worthy lily]

5arcsin(5 - 6) - 50arcsin(5-6)

[quick laurel]

You're close

$\int{\frac{x}{\sqrt{a^2-x^2}}dx} = -\sqrt{a^2-x^2}$

the integration changes for the second side of the equation however

[ocean seal]

Thasis

[worthy lily]

quotient rule?

what happened here

[quick laurel]

This same thing comes from the Table of Integrals as well. This is just a commonly known integration that saves me and you from having to reduce it ourselves haha

[worthy lily]

if I did quotient rule it would come out to that?

do I have to memorize this

because we are not allowed a formula sheet

the formula sheet they give us is very simple

[quick laurel]

I cannot imagine a calculus class that does not allow you a table of integration for integrations as the ones above

[worthy lily]

this is what we are allowed

[quick laurel]

I'm not saying that you are wrong

but during my time in calculus we always had one

[worthy lily]

this is all we are allowed

[quick laurel]

Because you will eventually have to learn about reductions and . . . there is no way that you could do those without the formula

[worthy lily]

I know

and the trig identities

[quick laurel]

Interesting.

[rigid smelt]

you dont quite need a tables of integrals for more "complicated" functions

since those should just be solved by hand instead of having to memorise stuff

[worthy lily]

that's the thing, we are given nothing really

that's the only thing we are allowed

[quick laurel]

Well, I must admit that is unfortunate

[rigid smelt]

yes, but i dont quite get the problem you are having?

[worthy lily]

I know

the calculus is really hard

that's the problem

[rigid smelt]

yes, everything is hard without practice

[gray isle]

you should be familiar with the methods used to evaluate them like
u-sub and/or trig sub

[worthy lily]

yes I am doing u sub

[rigid smelt]

just do more exercises and you should have an intuition for what you should do and when you should do it

[worthy lily]

and I am starting to learn trig sub, but even the trig sub, you have to memorize it

there is no formulas

but I guess there's 3 to remember and then the inverse is just -

• / +

[rigid smelt]

no, i recommend you remember the basic integrals and some trig identities

because those come in handy

[worthy lily]

basically I have 15 minutes to decide if I want to continue and study on my own and either do self paced online or show up in 4 months to do it next semester

or just keep going and really pick it up

what do you think?

[rigid smelt]

the fact that trig substitution is used is because you have many of the trig dentities to which you can apply

[gray isle]

knowing the derivation means you can get the result if you somehow forget the identity

[worthy lily]

so I have 5 - 50x / (sqroot(36 - 25x^2)

how do I solve this

I break it up into 2 pieces

5 / sqroot(36 - 25x^2)

and -50x / sqroot(36 - 25x^2)

guys I have 15 minutes to decide

[gray isle]

trig-sub for one and normal u-sub for the other

[worthy lily]

what do you think I should do?

should I drop or keep going

I've dropped so many times before

there is an option of self paced online

but I was thinking the paced class would get me working hard to keep up

but it moves so fast

[rigid smelt]

that would depend on you, if you feel like this is a bit too hard right now for you, you can go do some of the easier exercises

[worthy lily]

so I did u sub

and du = -50x

so du / -50x = du

[rigid smelt]

for which one?

[worthy lily]

and then sub that in for the 50x

and it cancels the 50x

and we are left with 1 / sqroot ( u )

[rigid smelt]

ok lets just slow down a bit, which one out of the two expressions you have attained are you trying to substitute?

or both?

[worthy lily]

the 2nd one

well both yea

I don't really know

I was thinking both

but when I do the left one, I get 50x again

do I think solve for x and sub it in to get it in u variables

[rigid smelt]

trig sub for the firt one and u-sub for the second one like ramonov mentioned

[worthy lily]

yea so I did u sub

[rigid smelt]

normal u-sub for the first one will not work very nicely

[gray isle]

for the left one, note that the numerator isn't close to the derivative of 36 - 25x^2
unlike the second fraction

[rigid smelt]

and for the second one i recommend substituting the expression inside the square, or even the whole square root if you like

[worthy lily]

so for the left one

what do you do?

[gray isle]

in cases like this, you would consider trig-sub (a special case of u-sub)

use a sub that would allow you to apply one of the pythaorean trig identities to express
36 - 25x^2
as a single term

[worthy lily]

can I ask you something

I have 10 minutes to decide if I want to keep going with this class

or should I do it self paced online

or study on my own and show up next semester

[gray isle]

have you already had a few lessons?
how far into this class are you

[worthy lily]

this is what the class is working on right now

2 weeks now

this is what the class is working on now

am I too far behind or can I catch up

I am only in 1 class I dropped everything else

[rigid smelt]

is this the first lesson on integration for this class?

[worthy lily]

no we started with integration

but now we are on this stuff

with trigonometric

[gray isle]

have you already done stuff with differentiation in a previous class?

[worthy lily]

yes

I have done Calc 1 , this is Calc 2

[rigid smelt]

how did you do in calc 1?

[gray isle]

it all depends on how much effort you're willing to put in

so your current issue atm seems to be just on trig-sub

[worthy lily]

I know derivatives

I'm on integration now

[gray isle]

there are plenty of vids on those

[worthy lily]

so I can either, keep doing it paced at school

or drop, study on my own and come back next semester after learning it in 4 months

[gray isle]

which watching a good video, you should have no trouble with within a few hours

[worthy lily]

or ask for permission to do class in a different school online, self paced have 10 months to finish

what do you think I should do?

[rigid smelt]

i do not recommend self-studying in this situation

[worthy lily]

why not?

[gray isle]

if you had a good understanding of normal u-sub, trig sub isn't a huge leap from that

[quick laurel]

$\int{\frac{x}{36-25x^2}} \to u=36-25x^2 \Rightarrow \frac{du}{dx}=-50x \Rightarrow \frac{1}{50x}du \longrightarrow -\frac{1}{50}\int{\frac{1}{\sqrt{u}}$

[rigid smelt]

well, because your school is providing you lessons, so if you can try hard enough, you can catch

[quick laurel]

does this much make sense @worthy lily

[rigid smelt]

at the same time, you are attending classes to get more knowledge, which is never a bad thing

[worthy lily]

yes

[rigid smelt]

you should only consider self-studying as the very last option

[worthy lily]

I have 5 minutes guys what should i do

yea the class moves fast though

and I've dropped it before

but now I'm ready to work hard

[ocean seal]

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

[rigid smelt]

ok, lets just say for a theoretical situation, you continue with this class, but you cant keep up, what will the school do?

[worthy lily]

I can drop later

but it will cost me $300

or if I go further

$600

[rigid smelt]

well, that's all i can say, myself, i would not self-study because having lessons with teachers who, you may call, experts are always a better option

if a tutor is not a viable option, i may recommend that you make lots of friends (especially those who are doing very well in the class) and ask for their help

as well as help from any place possible

[worthy lily]

shoudl I keep going?

I don't really go to school because I like studying from home

but I can do it from home basivcally

because all the work is online

except tests

[rigid smelt]

I, and i assume people here, can't answer that, it is your decision