If $f\left( x \right) = {\left( {\frac{{{x^2} + 5x + 3}}{{{x^2} + x + 2}}} \right)^x}$ then $\mathop {\lim }\limits_{x \to \infty } f\left( x \right)$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

f\left( x \right) = {\left( {\frac{{{x^2} + 5x + 3}}{{{x^2} + x + 2}}} \right)^x}

then

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

is equal to

View answer and explanation

Correct option: A

{e^4}

Option A (

{e^4}

) is correct because by rewriting the expression and taking the limit as x approaches infinity, the result is

{e^4}

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