Question

If $\text{f}(\text{x})=\frac{\text{x}^{\text{n}}-\text{a}^{\text{n}}}{\text{x}-\text{a}}$ for some constant, a, then f'(a) is equal to:

  1. $1$ 
  2. $0$ 
  3. Does not exist
  4. $\frac{1}{2}$ 

Answer

  1. Does not exist

Solution:

Given $\text{f}(\text{x})=\frac{\text{x}^{\text{n}}-\text{a}^{\text{n}}}{\text{x}-\text{a}}$

$\text{f'}(\text{x})=\frac{(\text{x}-\text{a})(\text{n.}\text{x}^{\text{n-1}}-(\text{x}^{\text{n}-\text{a}^{\text{n}}})1}{(\text{x}-\text{a})^{2}}$

So, $\text{f}(\text{a})=\frac{0}{0}$ = Does not exist.

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