Exercise $4.$ Compute the following two limits and two derivatives, which will be needed during Lab $2.$

$\underset{x0}{lim}\frac{1}{\sqrt[\phantom{2}]{1-x^2}},\frac{d}{dx}((1-x^2{)}^{-\frac{1}{2}})$

$\underset{x0}{lim}\frac{1}{x^2+1},\frac{d}{dx}((1+x^2{)}^{-1})$