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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
The value of $\mathop {\lim }\limits_{x \to 0} \,\left( {\frac{{{e^x} - 1}}{x}} \right)$ is
  • A
    $1/2$
  • B
    $\infty $
  • ✓
    $1$
  • D
    $0$
✓

Answer

Correct option: C.
$1$
c
(c) $\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{{e^x} - 1}}{x} = \mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{\left( {1 + \frac{x}{{1!}} + \frac{{{x^2}}}{{2!}} + ... - 1} \right)}}{x} = 1$.

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