Question

a^x - b^x / x as x tends to 0

Answer 1

Do you know the derivative of a^x wrt (with respect to) x?

Answer 2

yes

Answer 3

xlna?

Answer 4

would we apply l'hospital rule?

Answer 5

Good then write
\[\frac{a^x - b^x}{x} = \frac{a^x - 1}{x - 0} - \frac{b^x - 1}{x - 0}\]
Then notice the the limit of each of these terms is the derivate of a^x and b^x respectively evaluated at x=0.

Answer 6

yea now it is simple

Answer 7

thank u

Answer 8

Sure thing.