JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim \limits_{{x \rightarrow 1}} \frac{\int\limits_{1}^x|t-1| d t}{\sin (x-1)}

is equal to

View answer and explanation

Correct option: A

Option A (0) is correct. By applying L'Hopital's rule (or Leibnitz's rule) and evaluating the limit, we find that the limit is 0.

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\lim \limits_{{x \rightarrow 0}}\left(\frac{1}{x^2}-\operatorname{cosec}^2 x\right)

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\lim \limits_{{x \rightarrow \infty}} x\left(e^{1 / x}-1\right)

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