91Ó°ÊÓ

construct a table to find the indicated limit. $$\lim _{x \rightarrow-5} \frac{x^{2}-25}{x+5}$$

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied. $$\lim _{x \rightarrow 4}(6 x-21)^{3}$$

a. Find the slope of the tangent line to the graph of \(f\) at the given point. b. Find the slope-intercept equation of the tangent line to the graph of \(f\) at the given point. $$f(x)=\sqrt{x} \text { at }(16,4)$$

Use the definition of continuity to determine whether \(f\) is continuous at a. $$\begin{aligned}&f(x)=\left\\{\begin{array}{ll}\frac{x^{2}-4}{x-2} & \text { if } x \neq 2 \\\5 & \text { if } x=2\end{array}\right.\\\&a=2\end{aligned}$$

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied. $$\lim _{x \rightarrow 1}\left(2 x^{2}-3 x+5\right)^{2}$$

a. Find the slope of the tangent line to the graph of \(f\) at the given point. b. Find the slope-intercept equation of the tangent line to the graph of \(f\) at the given point. $$f(x)=\frac{1}{x} \text { at }(1,1)$$

construct a table to find the indicated limit. $$\lim _{x \rightarrow 0} \frac{2 x^{2}+x}{\sin x}$$

a. Find the slope of the tangent line to the graph of \(f\) at the given point. b. Find the slope-intercept equation of the tangent line to the graph of \(f\) at the given point. $$f(x)=\frac{2}{x} \text { at }(1,2)$$

Use the definition of continuity to determine whether \(f\) is continuous at a. $$\begin{aligned}&f(x)=\left\\{\begin{array}{ll}\frac{x^{2}-36}{x-6} & \text { if } x \neq 6 \\\13 & \text { if } x=6\end{array}\right.\\\&a=6\end{aligned}$$

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied. $$\lim _{x \rightarrow 2}\left(2 x^{2}+3 x-1\right)^{2}$$