Functions Question 22
Question: $ \underset{x\to \infty }{\mathop{\lim }}\frac{\sin x}{x}= $
[IIT 1975; MP PET 2004]
Options:
A) 1
B) 0
C) Does not exist
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to \infty }{\mathop{\lim }}\frac{\sin x}{x}, $ let $ x=\frac{1}{y} $ or $ y=\frac{1}{x}, $ so that $ x\to \infty \Rightarrow y\to 0 $
$ \therefore \underset{x\to \infty }{\mathop{\lim }}( \frac{\sin x}{x} )=\underset{y\to 0}{\mathop{\lim }}( y.\sin \frac{1}{y} )=\underset{y\to 0}{\mathop{\lim }}y\times \underset{y\to 0}{\mathop{\lim }}\sin \frac{1}{y}=0\times …=0 $
BETA
