$\mathop {\lim }\limits_{x \to \infty } x\sin \left( {\frac{2}{x}} \right)$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Application +4 | -1

\lim\limits_{x \to \infty } x\sin \left( {\frac{2}{x}} \right)

is equal to

View answer and explanation

Correct option: C

Option C (2) is correct because by substituting

u = \frac{2}{x}

, the limit transforms into a standard limit:

\lim_{u \to 0} \frac{\sin u}{u} = 1

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