Hmmm. Using L'hospitals rule, we have the value as
(a - 1/2 (1+x)^(-1/2))/2x
(1/4 (1+x)^(-3/2)/2
-> 1/8
So, I don't see how we can assign a value to a, because the limit is 1/8 for any value of a.
Am I missing something?
How do we find the value of a without using L'hospitals rule?
lim x-->0 [(1+ax) - (1+x)^(1/2)]/(x^2) } =(1/8)
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