If $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sin \frac{1}{x}\;\;\;\;\;x \ne 0}\\ {0\;\;\;\;\;\;x = 0} \end{array}} \right.$, then $\mathop {\lim }\limits_{x \to 0} f\left( x \right)$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Understanding +4 | -1

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {x\sin \frac{1}{x}\;\;\;\;\;x \ne 0}\\ {0\;\;\;\;\;\;x = 0} \end{array}} \right.

, then

\lim\limits_{x \to 0} f\left( x \right)

is equal to

View answer and explanation

Correct option: B

Option A (

\left( { - 6\;, - 3} \right) \cup \left( {3,6} \right)

) is correct because it represents the values of

x

that satisfy the inequality

3 < |x| < 6

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