Chapter 2: Problem 15
In Exercises 13-20, use graphs and tables to find the limits. $$\lim _{x \rightarrow-3^{-}} \frac{1}{x+3}$$
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In Exercises \(9-12,\) at the indicated point find (a) the slope of the curve, (b) an equation of the tangent, and (c) an equation of the tangent. (d) Then draw a graph of the curve, tangent line, and normal line in the same square viewing window. $$y=\frac{1}{x-1}\( at \)x=2$$
Multiple Choice Which of the following is an equation of the normal to the graph of \(f(x)=2 / x\) at \(x=1 ? \quad\) $$\begin{array}{ll}{\text { (A) } y=\frac{1}{2} x+\frac{3}{2}} & {\left(\text { B ) } y=-\frac{1}{2} x \quad \text { (C) } y=\frac{1}{2} x+2\right.} \\\ {\text { (D) } y=-\frac{1}{2} x+2} & {\text { (E) } y=2 x+5}\end{array}$$
In Exercises \(51 - 54 ,\) complete parts \(( a ) , (\) b) \(,\) and \(( c )\) for the piecewise-defined function. (a) Draw the graph of \(f .\) (b) Determine \(\lim _ { x \rightarrow c ^ { + } } f ( x )\) and \(\lim _ { x \rightarrow c ^ { - } } f ( x )\) (c) Writing to Learn Does \(\lim _ { x \rightarrow c } f ( x )\) exist? If so, what is it? If not, explain. $$c = 2 , f ( x ) = \left\\{ \begin{array} { l l } { 3 - x , } & { x < 2 } \\\ { \frac { x } { 2 } + 1 , } & { x > 2 } \end{array} \right.$$
In Exercises 47 and 48 , determine whether the graph of the function has a tangent at the origin. Explain your answer. $$f(x)=\left\\{\begin{array}{ll}{x \sin \frac{1}{x},} & {x \neq 0} \\ {0,} & {x=0}\end{array}\right.$$
Multiple Choice Find the average rate of change of \(f(x)=x^{2}+x\) over the interval \([1,3] .\) . \(\begin{array}{ll}{\text { (A) } y=-2 x} & {\text { (B) } y=2 x \text { (C) } y=-2 x+4} \\ {\text { (D) } y=-x+3} & {\text { (E) } y=x+3}\end{array}\)
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