Let $L = \mathop {\lim }\limits_{x \to 0} \,\,\frac{{a - \sqrt {{a^2} - {x^2}} - {x^2}/4}}{{{x^4}}},a > 0$. If $L$ is finite, then

JEE MATHEMATICS MCQ: LIMITS

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Let

L = \lim\limits_{x \to 0} \,\,\frac{{a - \sqrt {{a^2} - {x^2}} - {x^2}/4}}{{{x^4}}},a > 0

. If

L

is finite, then

View answer and explanation

Correct option: A

a = 2,L = \frac{1}{{64}}

Option A (

a = 2, L = \frac{1}{{64}}

) is correct because these values make the limit finite after using the binomial expansion.

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