JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

\lim \limits_{{x \rightarrow \infty}}\{\sqrt[3]{(x+a)(x+b)(x+c)}-x\}=

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Correct option: B

\frac{a+b+c}{3}

Option B,

\frac{a+b+c}{3}

, is correct because it is the result of rationalizing the expression and then taking the limit.

More Questions from LIMITS

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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)

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