# calculus

find the limit of f'(x) = 1/(√x) using the limit definition of derivative as x approaches 0.

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1. Given f(x)=1/√x
f'(x)
=Lim h->0 (f(x+h)-f(x))/h
=Lim h->0 (1/√(x+h)-1/√x))/h
subtract with common denominator
=Lim h->0 ((√x-√(x+h)/(h(√x √(x+h)))
multiply by conjugate of numerator, √(x)+√(x+h)
subtract and cancel h
Take limit h->0
=-1/x3/2

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