lim e^(-1/x)/x
x-> 0
lim e^(-1/x)/x
x-> infinity
i keep getting that they do not exist, and i need an actual value.
No idea what im doing wrong, any help much appreciated.
first one looks like..
approaching infinity / approaching zero, which just boosts the infinity into more infinitiness ;D
so its infinity..
it looks that way to me anyways without writing it down..
second one looks like...
top goes to 1/ bottom is x as x approaches infinity which would make it zero.
If you let u= 1/x your limits become $\displaystyle \lim_{u\rightarrow \infty} ue^{-u}$ and $\displaystyle \lim_{u\rightarrow 0}ue^{-u}$. The second of those is easy: setting u= 0 we get 0(1)= 0. For the first, you need to know that an exponential "dominates" and polynomial. $\displaystyle e^{-x}$ goes to 0 "faster" than u goes to infinity.