jee-advanced 2009 Q30

jee-advanced · India · paper1 Taylor series Limit evaluation using series expansion or exponential asymptotics

Let
$$L = \lim _ { x \rightarrow 0 } \frac { a - \sqrt { a ^ { 2 } - x ^ { 2 } } - \frac { x ^ { 2 } } { 4 } } { x ^ { 4 } } , \quad a > 0 .$$
If $L$ is finite, then
(A) $\quad a = 2$
(B) $\quad a = 1$
(C) $\quad L = \frac { 1 } { 64 }$
(D) $\quad L = \frac { 1 } { 32 }$

(A) and (C)

Let

$$L = \lim _ { x \rightarrow 0 } \frac { a - \sqrt { a ^ { 2 } - x ^ { 2 } } - \frac { x ^ { 2 } } { 4 } } { x ^ { 4 } } , \quad a > 0 .$$

If $L$ is finite, then\\
(A) $\quad a = 2$\\
(B) $\quad a = 1$\\
(C) $\quad L = \frac { 1 } { 64 }$\\
(D) $\quad L = \frac { 1 } { 32 }$

Paper Questions

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