JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

Let

{a}_m

be the

{m}^{\text {th }}

term of the sequence

\left(\frac{2^2}{1^2}-\frac{2}{1}\right)^{-1},\left(\frac{3^3}{2^3}-\frac{3}{2}\right)^{-2},\left(\frac{4^4}{3^4}-\frac{4}{3}\right)^{-3}, \ldots .

. , then the value of

\lim \limits_{{m \rightarrow \infty}}\left(a_m\right)^{\frac{1}{m}}

is equal to

View answer and explanation

Correct option: C

\frac{1}{{e}-1}

Option C,

\frac{1}{{e}-1}

, is correct because the limit of the given expression as m approaches infinity simplifies to this value using properties of limits and the definition of e.

More Questions from LIMITS

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

is equal to

\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cos x}{(1-\sin x)^{2 / 3}}=

The value of

\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)

is equal to If

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

, then the value of

f^{\prime}(0)

is equal to

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

equals