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When h tends to 0 both the

When h tends to 0 both the numerator and the denominator of (f(x+h)-f(x))/h tend to 0. This does not mean that the whole expression tends to 0. As an example take f(x)=2x. Then (f(x+h)-f(x))/h=(2(x+h)-2x)/h = 2h/h = 2.


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