JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Analyzing +4 | -1

\lim _{x \rightarrow 0} \frac{x\left(e^{\left(\sqrt{1+x^2+x^4}-1\right) / x}-1\right)}{\sqrt{1+x^2+x^4}-1}

View answer and explanation

Correct option: B

is equal to 1

Option B (is equal to 1) is correct because after substituting

t = \frac{{\sqrt{{1 + x^2 + x^4}} - 1}}{{x}}

, the limit simplifies to the standard limit

\lim_{{t \rightarrow 0}} \frac{{e^t - 1}}{{t}} = 1

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