91Ó°ÊÓ

find the limit $$ \lim _{x \rightarrow 2} \frac{2-x}{x^{2}-4} $$

Sketch the graph of the function and describe the interval(s) on which the function is continuous. \(f(x)=\left\\{\begin{array}{ll}x^{2}-4, & x \leq 0 \\ 2 x+4, & x>0\end{array}\right.\)

Find an equation of the tangent line to the graph of \(f\) at the point \((2, f(2)) .\) Use a graphing utility to check your result by graphing the original function and the tangent line in the same viewing window. $$ f(x)=x \sqrt{x^{2}+5} $$

Find an equation of the tangent line to the graph of \(f\) at the point \((2, f(2)) .\) Use a graphing utility to check your result by graphing the original function and the tangent line in the same viewing window. $$ f(x)=\sqrt{x^{2}-2 x+1} $$

Use the limit definition to find an equation of the tangent line to the graph of \(f\) at the given point. Then verify your results by using a graphing utility to graph the function and its tangent line at the point. $$ f(x)=\frac{1}{x} ;(1,1) $$

find \(f^{\prime}(x)\). $$ f(x)=\frac{4 x^{3}-3 x^{2}+2 x+5}{x^{2}} $$

find the limit $$ \lim _{t \rightarrow 4} \frac{t+4}{t^{2}-16} $$

find \(f^{\prime}(x)\). $$ f(x)=\frac{-6 x^{3}+3 x^{2}-2 x+1}{x} $$

Find an equation of the tangent line to the graph of \(f\) at the point \((2, f(2)) .\) Use a graphing utility to check your result by graphing the original function and the tangent line in the same viewing window. $$ f(x)=\left(4-3 x^{2}\right)^{-2 / 3} $$

Find the constant \(a\) (Exercise 45\()\) and the constants \(a\) and \(b\) (Exercise 46 ) such that the function is continuous on the entire real line. \(f(x)=\left\\{\begin{array}{ll}2, & x \leq-1 \\ a x+b, & -1