Question

Text says the limit of (a^h - 1)/h as h approaches 0 is equal to the derviative of f at 0. I don't understand how this works out. Please explain. Thank you!

Answer 1

@ikram002p

Answer 2

its cuz of LH rule

Answer 3

or u wanna use definition to prove it ?

Answer 4

i think they want to use the limit definition of derivative

Answer 5

f(x) = a^x

Answer 6

i think so as well .

Answer 7

its like direct ..

Answer 8

\[f'(a) = \lim\limits_{h\to a} \dfrac{f(h)-f(a)}{x-a}\]

Answer 9

substitute

f(h) = a^h
and a = 0