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Limits and Derivatives — Maths STD 11 Science — Question

CBSE 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
    $0$
  • ✓
    Does not exist
  • D
    $\frac{1}{2}$
✓

Answer

Correct option: C.
Does not exist
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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