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Derivatives — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives1 Mark
MCQ
If $\text{f(x)}=\frac{\text{x}^\text{n}-\text{a}^\text{n}}{\text{x}-\text{a}},$ then $\text{f}'\text{(a)}$ is:
  • A
    $1$
  • B
    $0$
  • C
    $\frac{1}{2}$
  • ✓
    $\text{dose not exist}$
✓

Answer

Correct option: D.
$\text{dose not exist}$
Given: $\text{f(x)}=\frac{\text{x}^\text{n}-\text{a}^\text{n}}{\text{x}-\text{a}}$
Now, f(x) is not difined at x = a. Therefore, f(x) is not differentiable at x = a.
So, f'(a) dose not exist.
Hence, the correct answer is option (d).

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