Let $f:R \to R$ be appositive increasing function with $\mathop {\lim }\limits_{x \to \infty } \frac{{f\left( {3x} \right)}}{{f\left( x \right)}} = 1$. Then, $\mathop {\lim }\limits_{x \to \infty } \frac{{f\left( {2x} \right)}}{{f\left( x \right)}}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

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Let

f:R \to R

be appositive increasing function with

\lim\limits_{x \to \infty } \frac{{f\left( {3x} \right)}}{{f\left( x \right)}} = 1

. Then,

\lim\limits_{x \to \infty } \frac{{f\left( {2x} \right)}}{{f\left( x \right)}}

is equal to

View answer and explanation

Correct option: A

Option A (1) is correct because, by the Sandwich theorem, the limit of f(2x)/f(x) as x approaches infinity is squeezed between 1 and the limit of f(3x)/f(x), which is given as 1.

JEE MATHEMATICS MCQ: LIMITS

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