The value of $\mathop {\lim }\limits_{x \to \infty } {\left\{ {\frac{{a_1^{1/x} + a_2^{1/x} + \ldots + a_n^{1/x}}}{n}} \right\}^1}$, is

${a_1} + {a_2} + \ldots + {a_n}$

${e^{{a_1} + {a_2} + \ldots + {a_n}}}$

$\frac{{{a_1} + {a_2} + \ldots + {a_n}}}{n}$

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Understanding +4 | -1

The value of

\lim\limits_{x \to \infty } {\left\{ {\frac{{a_1^{1/x} + a_2^{1/x} + \ldots + a_n^{1/x}}}{n}} \right\}^1}

, is

View answer and explanation

Correct option: D

{a_1}{a_2} \ldots \ldots {a_n}

Option D (

{a_1}{a_2} \ldots \ldots {a_n}

) is correct because it uses the limit properties and exponential/logarithmic transformations to simplify the expression.

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