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Limits Continuity and Differentiability question

2009 · Shift 1 · Q37

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2009 · Shift 1 · Q37

Limits Continuity and Differentiability question

2009 · Shift 1 · Q37

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let

L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a \gt 0

. If L is finite, then

A
$a = 2$
B
$a = 1$
C
$L = {1 \over {64}}$
D
$L = {1 \over {32}}$

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