The value of $\mathop {\lim }\limits_{x \to \infty } {a^x}\sin \left( {\frac{b}{{{a^x}}}} \right)$ is $(a > 1)$

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

The value of

\lim\limits_{x \to \infty } {a^x}\sin \left( {\frac{b}{{{a^x}}}} \right)

(a > 1)

View answer and explanation

Correct option: C

b

Option C (

b

) is correct because as

x

approaches infinity,

\frac{b}{{{a^x}}}

approaches 0, and the limit can be evaluated using the small angle approximation for sine.

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