JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Understanding +4 | -1

f(x)=\int\limits_{1}^x \frac{\sin t}{t} d t

, then

\lim \limits_{{x \rightarrow \infty}} f^{\prime}(x)

is equal to

View answer and explanation

Correct option: A

Option A (0) is correct because as x approaches infinity, the function f'(x) =

\frac{{\sin t}}{{t}}

approaches 0, due to the denominator growing without bound while the numerator oscillates between -1 and 1.

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\lim\limits_{n \to \infty } {\left( {1 + \sin \frac{a}{n}} \right)^n}