Question

Please help me evaluate the following limit:
Kindly find attached

Answer 1

Please don't use L’Hˆopital’s Rule. Kindly use another approach. Thanks!

Answer 2

Any particular reason that L'Hospital's Rule cannot be used? @fireofsky

Answer 3

No. It is just I want to know the way without using L’Hˆopital’s Rule. Otherwise it'll be very easy. Right?

Answer 4

Do you know derivatives?

Answer 5

Yes. I know

Answer 6

This is f'(0) for a certain f(x). Which f(x) and why?

Answer 7

just plug in x=y^3-1

sowhat will be numerator ?

Answer 8

also note that when x->0, y->1

Answer 9

I see. thank you so much.!!!

Answer 10

\[
f(x)=\sqrt[3]{x+1}\\
\]

Answer 11

\[
f'(x)=\frac{1}{3 (x+1)^{2/3}}\\
f'(0)=\frac 1 3
\]

Answer 12

can u show more details please?

Answer 13

okay. but why? not using L'Hospital's Rule