Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow \infty} \frac{x^n}{ e ^x}=0$ 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) Applying L-Hospital's rule, we get $\lim _{x \rightarrow \infty} \frac{x^{ n }}{ e ^x}=\lim _{x \rightarrow \infty} \frac{ n x^{ n -1}}{ e ^x}$ $=\lim _{x \rightarrow \infty} \frac{ n ( n -1) x^{ n -2}}{ e ^x}=\lim _{x \rightarrow \infty} \frac{ n !}{ e ^x}=\frac{ n !}{\infty}=0$, where n is any whole number... $[\because n !$ is defined for all positive integers including zero]
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