Search any question & find its solution
Question:
Answered & Verified by Expert
What is the value of $\lim _{x \rightarrow \infty} \frac{\sin x}{x}$ ?
Options:
Solution:
2210 Upvotes
Verified Answer
The correct answer is:
0
Given limit is: $\lim _{x \rightarrow \infty} \frac{\sin x}{x}$
Let, $\mathrm{x}=\frac{1}{\mathrm{~h}}$ and as $\mathrm{x} \rightarrow \infty, \mathrm{h} \rightarrow 0$
$\therefore \lim _{x \rightarrow \infty} \frac{\sin x}{x}$ change to : $\lim _{h \rightarrow 0} h \sin \frac{1}{h}$
$=0$ (value of $\sin \frac{1}{\mathrm{~h}}$ is finite as it lies between $-1$ and 1 )
Let, $\mathrm{x}=\frac{1}{\mathrm{~h}}$ and as $\mathrm{x} \rightarrow \infty, \mathrm{h} \rightarrow 0$
$\therefore \lim _{x \rightarrow \infty} \frac{\sin x}{x}$ change to : $\lim _{h \rightarrow 0} h \sin \frac{1}{h}$
$=0$ (value of $\sin \frac{1}{\mathrm{~h}}$ is finite as it lies between $-1$ and 1 )
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.