Let `L=("lim")_(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i t e ,t h e n` `a=2` (b) `a=1` `L=1/(64)` (d) `L=1/(32)`

Answer

A, C

Explanation

`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)`.