derivatives

[wet thunder]

Can someone tell me how to do this

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[sly rose]

I’d start with turning it into the more standard definition of derivative and say x +h =2pi

[green sleet]

I'd venture to say that's not necessary

a friend of mine has that formula but was never taught the definition of a limit lol

[sly rose]

I just know with x+h we can do double angle

From here it solves really nicely

This is just a nasty limit to evaluate without using the Taylor series def/l’hopitals which all require knowing the derivative.

[green sleet]

any closer yet?

because atp im wasting paper lol

@wet thunder what have you attempted so far

[sly rose]

It depends how we define the trig functions

[wet thunder]

Hi sorry I just got home

[sly rose]

I think we can probably get away with just saying that sin(u)/u is 1

Have you done that as a standard def erveenkm

[green sleet]

can someone get that bot to rotate

,rotate

[green sleet]

your solution is interesting

your answer is correct

that much is clear

[sly rose]

It’s not an answer is it just part of some working

[green sleet]

oh I thought they just divided by (sin 2pi - sin x), leaving 1

[sly rose]

I mean the questions probably just asking you to recognise it’s the derivative of sin at 2pi tbh and just knowing it’s cos(2pi)

[green sleet]

not sure if that's even legal though lol

[wet thunder]

I did this but I’m not getting the right answer

[sly rose]

How did you get from a to b

If you used the quotient rule you’ve used the derivative of sin to work out the derivative of sin

[wet thunder]

I did the quotient rule but I don’t know what that means

[sly rose]

Right okay

Do you know what the question is asking in words

Asin if you take the limit what do you get

[wet thunder]

Find the limit as it approached 2pi

[sly rose]

What does the limit mean graphically

[wet thunder]

What y value is the the line approaching going toward x ?

[sly rose]

Not quite

Have you seen either of these before

[wet thunder]

The first one

[sly rose]

Right cool

What does the first one mean

[wet thunder]

Using derivative to find limit

[green sleet]

the other way around right?

[wet thunder]

Oh sorry

[sly rose]

Yeye it’s the derivative

Now if we look at what your questions is asking

It’s asking the limit as x approaches 2pi

Do we see how this is also the gradient

The difference in y divided by the difference in x

Then the limit as the difference in x approaches zero

[wet thunder]

Gradient is slope?

[sly rose]

Yep

[wet thunder]

So we are trying to find gradient /slope when limit is approaching 2pi

[sly rose]

Yep

So what the question is really asking is the derivative of sin at 2pi

[green sleet]

out of curiousty, does L'Hôpital's rule mean anything to you?

[wet thunder]

Yes I learned it

[green sleet]

@sly rose bollucks

[wet thunder]

So cos (2pi)

[sly rose]

Yep

Cos(2pi)

[wet thunder]

I get 1 with that isn’t answer -1?

[wet thunder]

😭

[green sleet]

try using L'Hopitals here

[sly rose]

The answer should be 1

[wet thunder]

I get 0

[green sleet]

show your work please

[sly rose]

I wouldn’t use lhopital it feels abit overkill

And unjustified

[sly rose]

Yes the answer is 1 is their answer wrong

[wet thunder]

My friend did the assignment and the correct answer was -1 I just don’t know how to get there

[sly rose]

It should be 1

[green sleet]

wolframalpha tells me 1 and so does desmos

but I get a different answer from microsoft's math solver

that gives -1

[sly rose]

Oh I’m having a moment here lol

Yes it’s minus 1, 1 sec lemme show

[green sleet]

the same

where the hell is my mistake

[sly rose]

The denominators negative from the derivative

[green sleet]

more likely, I'm just blind kek

or I flipped it around sinx-sin2pi

that's my mistake

[wet thunder]

So it’s not derivative of sin at 2pi?

[green sleet]

if they know it and it works...

[sly rose]

It’s negative the derivative at 2pi

[wet thunder]

What’s the work to get to there?

Ohhh wait

[sly rose]

Well you see from the diagram here

So we can see that this is the definition of gradient

The thing you are given is almost there

Just the denominator is flipped

So we just flip it back

[wet thunder]

Sorry I saw u flipped the denominator but I didn’t know why so u put the negative on the outside

So it’s -cos from there

[sly rose]

Yep

[wet thunder]

Okay I think I get it now

And u can do it with the numerator too?

[sly rose]

Aight sorry I went about of a long way around it

Well the numerators the right way round

[wet thunder]

U can’t do denominator?

[sly rose]

Nono by taking the negative out of the denominator

We are left with the definition of the derivative

So our answer is -f’(2pi)

[wet thunder]

How come after taking the negative out we don’t use the function anymore and just the sin

[sly rose]

What do you mean?

[fallow wasp]

ayo what about integrate ima stuck with two question here as well

i have to set u and du isnt it

[sly rose]

Mk you should start a new post in #1015578016606343218

[fallow wasp]

oh okok

[sly rose]

Go on sorry

[wet thunder]

It’s okay

I mean so we take the negative out but then take the derivative of sin, why don’t we use the f(2pi) - f(x) / x - 2pi anymore

[sly rose]

We are using that but once we take out a negative

You can use the fact that, that is by definition the derivative

And just say okay so it’s negative of the derivative

[wet thunder]

Maybe this is something I haven’t learned yet