Question

Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 e3x − 1 − 3x x2

Answer 1

It looks like the limit is

`\displaystyle \lim_(x\to0) (e^(3x) - 1 - 3x)/(x^2)`

L'Hôpital's rule works in this case; applying it twice gives

`\displaystyle \lim_(x\to0) (e^(3x) - 1 - 3x)/(x^2) = \lim_(x\to0) (3e^(3x) - 3)/(2x) = \lim_(x\to0) (9e^(3x))/(2) = \boxed{\frac92}`