JEE MATHEMATICS MCQ: LIMITS

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\lim \limits_{{x \rightarrow \pi / 4}} \frac{4 \sqrt{2}-(\cos x+\sin x)^5}{1-\sin 2 x}=

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Correct option: A

5 \sqrt{2}

Option A (

5 \sqrt{2}

) is correct because the limit is evaluated by using trigonometric identities and substitution to simplify the expression.

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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}