ISRO2016-EC Mathematics

Question

The value of $\lim _{x \rightarrow 8}\left(\frac{x^{1 / 3}-2}{x-8}\right)$ is

1. $1/4$
2. $1/8$
3. $1/12$
4. $1/16$

Answer 1

This is the case of 0/0. This can be solved using L'Hospital's rule. Differentiate both numerator and denominator w.r.t. x separately. After differentiation we will get :

limit (x->8) ((1/3)X^(-2/3))
now put the value of x in equation as it is free from 0/0 case. After solving it the answer will be 1/12.

Answer 2

https://gateoverflow.in/?qa=blob&qa_blobid=9931864936147590124

Answer 3

Apply L hospital,
U will get 1 /12