Evaluating limits analytically:

a$)\underset{x-1}{lim}\frac{\sqrt[\phantom{2}]{x+2}-1}{x+1}$

b$)\underset{-1}{lim}\frac{1-cos}{sin}$

c$)\underset{h0}{lim}\frac{\frac{1}{(x+h{)}^2}-\frac{1}{x^2}}{h}$

Determine the continuity of the following function $f(x)$ at $x=1.$ Classify the discontinuity as removable, jump, or infinite if applicable.

$f(x)=\{\begin{array}{cc}-x^2,& x1\\ 3,& x=1\end{array}$

An object moving in a straight$-$line travels $s(t)$ kilometers in $t$ hours, where $s(t)=8t^2+2t$

a$)$ How far has the object traveled in $4$ hours?

b$)$ Estimate the object's instantaneous velocity when $t=4?$

Find all the vertical asymptotes the function $f(x)=\frac{3x^2-6}{x^2-2x}$ using limits$,$ if possible. Show work to get full credit.

Prove that $\underset{x0}{lim}{x}^{2}cos(\frac{}{x^2})=0$