Evaluate the limit:

Question

lim 5e^x - 5e^x+h / 3h

h--> 0

Answer 1

Recall that f'(x) = lim_h→0 [(f(x+h - f(x)) / h]

Let f(x) = e^x. So, f(x+h) = e^x+h.

Then, lim_h→0 [5(e^x - e^x+h) / (3h) ] = -(5/3)lim_h→0 [(e^x+h - e^x) / h ] = -(5/3)(e^x)' = -(5/3)e^x

Answer 2

Can you please rewrite the expression in a more understandable way? It is not clear what you mean.