Functions Question 214
Question: $ \underset{x\to 0}{\mathop{\lim }},\sin ( \frac{1}{x} ) $ is
[SCRA 1996]
Options:
A) 0
B) 1
C) ?1
D) Does not exist
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to {0^{-}}}{\mathop{\lim }},f(x)=\underset{h\to 0}{\mathop{\lim }},f(0-h) $ $ =\underset{h\to 0}{\mathop{\lim }}\sin ,( \frac{-1}{h} )=\underset{h\to 0}{\mathop{\lim }},-\sin \frac{1}{h} $ = ? 1 (finite number lies between ? 1 to 1) $ \underset{x\to {0^{+}}}{\mathop{\lim }},f(x)=\underset{h\to 0}{\mathop{\lim }},f(0+h) $ $ =\underset{h\to 0}{\mathop{\lim }},\sin ( \frac{1}{h} ) $ = (finite number lies between 0 to 1) $ \because \underset{x\to {0^{-}}}{\mathop{\lim }},f(x)\ne \underset{x\to {0^{+}}}{\mathop{\lim }},f(x) $ ; \ $ \underset{x\to 0}{\mathop{\lim }},\sin ( \frac{1}{x} ) $ does not exist.
BETA
