Question

L'Hopital

Answer 1

\[\frac{ 2-2\cos( \pi x) }{ (x-1)^2 }\]

Answer 2

I wanted to know do I have to change the form so I get 0/0 or can I take the derivative as is?

Answer 3

sorry limit as x approaches 1

Answer 4

I know with direct substitution it is 1/0 but in order to do L'hopital it has to be in the form of 0/0 or infinity/infinity right?

Answer 5

correction with direct substitution it is 4/0

Answer 6

Multiply this by \[\frac{1+cos(\pi x)}{1+cos(\pi x)}\]

Answer 7

then you will get a limit 0/0

Answer 8

and just apply L'Hospital

Answer 9

ok thank you

Answer 10

np

Answer 11

If you plug in \(1\), you get the \(0/0\) form, so you can differentiate it as is.

Answer 12

Hmmm, I guess it isn't an indeterminate form as it is, weird.

Answer 13

@M4thM1nd can I take the ln of the imit to make it easier to differentiate?

Answer 14

because when I did l'hopital the derivative was still 0/0

Answer 15

well if:
\[L = lim_{x \rightarrow 1} \frac{2*(1-cos(\pi x))}{(x-1)^2}\], you can take the ln() of both sides

Answer 16

that's not the case here. Is there any other way I can clean it up to make it faster or is it just going to be a long differentiation?

Answer 17

i don't see other way of making this faster

Answer 18

alright thank you

Answer 19

Actually it is solved very fast, just two differentiation