ISI-2014-5

Question

The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$

• A. $\text{is 0}$
• B. $\text{is 1}$
• C. $\text{is 2}$
• D. $\text{does not exist}$

Answer 1

option a

Well see function sin(1/x) is bounded between [−1,1] and as

limx→0 xsin(1/x)

the value of x will also go to zero hence value of limit is 0

Comments

How ? please explain abhishekmehta4u.

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bro A is correct...when we put x = 0 then it becomes 0*(any number between -1 and 1 ) = 0 bcoz range of sinθ is from -1 to +1  ..

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yes 0 should be the answer

Answer 2

It is option B

Comments

lim x-->0 sin(1/x)/1/x is not equal to 1.

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Yeah, you are right. My mistake. Then it should be 0.

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GOOD ATTEMPT!