If $a,b,c,d$ are positive, then $\mathop {\lim }\limits_{x \to \infty } \,{\left( {1 + \frac{1}{{a + bx}}} \right)^{c + dx}} = $

${e^{\left( {c + d} \right)/a + b}}$

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

a,b,c,d

are positive, then

\lim\limits_{x \to \infty } \,{\left( {1 + \frac{1}{{a + bx}}} \right)^{c + dx}} =

View answer and explanation

Correct option: A

{e^{d/b}}

Option A (

{e^{d/b}}

) is correct because the limit can be rewritten in the form of

e

raised to the power of another limit, which simplifies to

{e^{d/b}}

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