If $\lim _{x \rightarrow 0}\left(1+a x+b x^2\right)^{1 / x}=e^3$, then

$a=3 / 2$ and $b$ is any real number

$b=3$ and $a$ is any real number

$a=1$ and $b$ is any real number

JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

\lim _{x \rightarrow 0}\left(1+a x+b x^2\right)^{1 / x}=e^3

, then

View answer and explanation

Correct option: A

a=3

and

b

is any real number

Option A (

a=3

and

b

is any real number) is the correct answer because the limit simplifies to

e^a

, which must equal

e^3

, therefore

a=3

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