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Let L=lim(x->0)(a-sqrt(a^2-x^2)-(x^2)/4...

Let `L=lim_(x->0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0`. If` L` is finite ,then` (a)``a=2` (b) `a=1` (c)`L=1/(64)` (d) `L=1/(32)`

Text Solution

Verified by Experts

`L=underset(xto0)lim(a-sqrt(a^(2)-x^(2))-(x^(2))/(4))/(x^(4))`
`=underset(xto0)lim((1)/(x^(2)(a+sqrt(a^(2)-x^(2))))-(1)/(4x^(2)))`
`=underset(xto0)lim((4-a)-sqrt(a^(2)-x^(2)))/(4x^(2)(a+sqrt(a^(2)-x^(2))))`
Numerator` to" if "a=2` and then `L=(1)/(64)`.
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