If $\displaystyle t = \frac{1}{x}$ then
a) Explain why $\displaystyle\lim_{x \to 0^-}f(x)$ is equivalent to $\displaystyle\lim_{t \to -\infty}f\left(\frac{1}{t}\right)$
b) Using that, rewrite $\displaystyle\lim_{x \to 0^-} e^\frac{1}{x}$ as equivalent limit involving $t$ only. Evaluate the corresponding limit.
c) Use a similar technique to evaluate $\displaystyle\lim_{x \to \pm\infty} \ln\left(\frac{2}{x^3}\right)$
On a, I thought that they are equivalent because $f(x)$ is the inverse of $t$, is that correct?
On b, I get $\displaystyle\lim_{x \to 0^-} e^t$. How would I solve this limit? Isn't it the $t$'th root of $e$? Im confused...
And c just confuses me to begin with. How would I calculate that limit? I don't know where to start on that one and just need some help with getting my mind around it.
Thanks