Question

Compute the following limits using l'Hospital's rule if appropriate.(a>0)
Use INF to denote ∞ and -INF to denote −∞.

limx→0 [(a^x−7^x)/8x]

Answer 1

Since limx→0 [(a^x−7^x)/8x] goes to the indeterminate form 0/0, use L'Hopital's rule to take the derivative of both the top and the bottom.

So taking the derivative of both the numerator and the denominator:
limx->0 [(ln(a) * a^x - ln 7 * x)/8]

setting x to 0 the answer is (ln(a) - ln(7))/8