JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

\operatorname{Lim}_{x \rightarrow 0} \frac{\ln (3+x)-\ln (3-x)}{x}=k

, the value of

k

View answer and explanation

Correct option: A

\frac{2}{3}

Option A (

\frac{2}{3}

) is correct because it is the limit of the given expression as x approaches 0, evaluated using L'Hôpital's rule or series expansion.

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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_{h \to 0} 2\left\{ {\frac{{\sqrt 3 \sin \left( {\frac{\pi }{6} + h} \right) - \cos \left( {\frac{\pi }{6} + h} \right)}}{{\sqrt 3 h\left( {\sqrt 3 \cos \,h - \sin \,h} \right)}}} \right\}

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

f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}

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