Question

Hi, I am attempting to find the limit of x/10^x using L'Hopital's rule, and I know the answer should be 0, but I'm not sure how to get there.

Answer 1

well the L'Hopital's rule is simple: lim of f(x)/g(x) when x tends to zero or infinite is = samelimit of f'(x)/g'(x)
You have the limit of x = infinite and the limit of 10^x = infinite so it's infinite/infinite

But, the derivative of x is 1 and the derivative of 10^x is (10^x).log(10), then you have 1/(10^x).log(10). the limit of 1 is 1, and the limit of (10^x).log(10) is infinite. 1/infinite tends to 0