Question

Mark the correct alternative in each of the following:

If $f\left(x\right)=\frac{x^n-a^n}{x-a}$, then $f\text{'}\left(a\right)$ is

(a) 1 (b) 0 (c) $\frac{1}{2}$ (d) does not exist

Answer 1

Given: $f\left(x\right)=\frac{x^n-a^n}{x-a}$

Now, f(x) is not defined at x = a. Therefore, f(x) is not differentiable at x = a.

So, $f\text{'}\left(a\right)$ does not exist.

Hence, the correct answer is option (d).