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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 $\text{f}(\text{x})=1+\text{x}+\frac{\text{x}^{2}}{2}+.....+\frac{\text{x}^{100}}{100}$ then $f'(1)$ is equal to:
  • A
    $\frac{1}{100}$
  • ✓
    $100$
  • C
    does not exist
  • D
    $0$
✓

Answer

Correct option: B.
$100$
Given $\text{f}(\text{x})=1+\text{x}+\frac{\text{x}^{2}}{2}+.....+\frac{\text{x}^{100}}{100}$
$\text{f}(\text{x})=1+\frac{2\text{x}}{2}+......+\frac{100\text{x}}{100}$
$\therefore \text{f'}(1)=1+11+....+1=100$

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