Question

Evaluate the limit using l'hospitals rule. lim->0 (3^x-6^x)/x. Do not know where to even begin on this one... please help.

Answer 1

If you don't even know where to begin, you must not have read the section on this topic. It says that

the limit of f(x)/g(x) = f'(x)/g'(x)

so, your limit is just

(ln3 * 3^x - ln6 * 6^x)/1
= (ln3-ln6)
= ln(3/6) = -ln2