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AMPLE Iff (x) is differentiable at xa, find limxma-x-a

Answer»

since f(x) is differentiable so, f'(x) exists..

now the limit is 0/0 so, using L.H rule

lim(x→a) [x²f(a)-a²f(x)]/(x-a)

so, = [2xf(a) - a²f'(x)]/1 = 2af(a) - a²f'(a)

so, the value is. a[2f(a)-af'(a)]


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