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Limits and Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits and Derivatives1 Mark
MCQ
Choose the correct answer.
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:
  • A
    $1$ 
  • B
    $0$ 
  • C
    Does not exist
  • D
    $\frac{1}{2}$ 
✓

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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