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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {\lim }\limits_{x \to \infty } \frac{{{x^n}}}{{{e^x}}} = 0$ for
  • A
    No value of $n$
  • ✓
    $n$ is any whole number
  • C
    $n = 0$ only
  • D
    $n = 2$ only
✓

Answer

Correct option: B.
$n$ is any whole number
b
(b) $\mathop {\lim }\limits_{x \to \infty } \frac{{{x^n}}}{{{e^x}}} = \mathop {\lim }\limits_{x \to \infty } n\frac{{{x^{n - 1}}}}{{{e^x}}} = ......$

$ = \mathop {\lim }\limits_{x \to \infty } \frac{{n\,\,!}}{{{e^x}}} = \frac{{n\,\,!}}{\infty } = 0$,

where $n$ is any whole number

$( \because n! $ is defined for all positive integers including zero).

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