I'm at the stage of my calculus course where we've just been introduced to the logarithm and exponential functions and I'm having some trouble evaluating limits in the form of exponential functions.
lim as x->0 (exp(2x)+2x)^1/x, so far i've gotten up to lim x->0 (1+2x/exp(2x))^1/x*e^2
lim as x->0 (((1+x+x^2)^1/x)/exp(1))^1/x
I know that the number e can be defined as the limit as x goes to 0 of (1+x)^1/x, but I'm at a complete loss when it comes to applying this to evaluating the given limits.
Any help would be appreciated.