Problem $1$: Use a table of inputs and outputs to estimate the limit numerically or state that it does not exist.

a$.\underset{x1}{lim}\frac{e^x-e}{lnx}$

b$.\underset{0}{lim}\frac{cos-1}{}($Make sure to use radian measure$)$

c$.\underset{x-}{lim}(5x^{-2}+x^5)$

d$.\underset{x{4}^{+}}{lim}\frac{3x-4}{x^2-16}$

e$.\underset{x0}{lim}\frac{2sinx}{|x|}($Notes: $|x|$ is either $-x$ if $x<mn>0</mn>$ or $x$ if $x>0$ and make sure to use radian measure$).$