91Ó°ÊÓ

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied. $$\lim _{x \rightarrow-2} 7 x^{2}$$

construct a table to find the indicated limit. $$\lim _{x \rightarrow 3} \frac{1}{x-2}$$

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. $$f(x)=2 x^{2}-x \text { at }(2,6)$$

Use the definition of continuity to determine whether \(f\) is continuous at a. $$\begin{aligned}&f(x)=\frac{x+5}{x-5}\\\&a=5\end{aligned}$$

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

construct a table to find the indicated limit. $$\lim _{x \rightarrow 4} \frac{1}{x-3}$$

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. $$f(x)=3 x^{2}+x \text { at }(1,4)$$

construct a table to find the indicated limit. $$\lim _{x \rightarrow 0} \frac{x}{x^{2}+1}$$

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. $$f(x)=2 x^{2}+x-3 \text { at }(0,-3)$$

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied. $$\lim _{x \rightarrow 5}\left(x^{2}-3 x-4\right)$$