Chapter 2: Problem 13
In Exercises \(7 - 14 ,\) determine the limit by substitution. Support graphically. $$\lim _ { x \rightarrow - 2 } ( x - 6 ) ^ { 2 / 3 }$$
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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$$
Exploring Properties of Limits Find the limits of \(f, g,\) and \(f g\) as \(x \rightarrow c .\) (a) $$f(x)=\frac{1}{x}, \quad g(x)=x, \quad c=0$$ (b) $$f(x)=-\frac{2}{x^{3}}, \quad g(x)=4 x^{3}, \quad c=0$$
In Exercises \(19 - 28 ,\) determine the limit graphically. Confirm algebraically. $$\lim _ { x \rightarrow 0 } \frac { 5 x ^ { 3 } + 8 x ^ { 2 } } { 3 x ^ { 4 } - 16 x ^ { 2 } }$$
In Exercises \(67 - 70\) , use the following function. \(f ( x ) = \left\\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.\) Multiple Choice What is the value of \(\lim _ { x \rightarrow 1 ^ { - } } f ( x ) ?\) \(\begin{array} { l l l l l } { \text { (A) } 5 / 2 } & { \text { (B) } 3 / 2 } & { \text { (C) } 1 } & { \text { (D) } 0 } & { \text { (E) does not exist } } \end{array}\)
Multiple Choice Which of the following points of discontinuity of $$f(x)=\frac{x(x-1)(x-2)^{2}(x+1)^{2}(x-3)^{2}}{x(x-1)(x-2)(x+1)^{2}(x-3)^{3}}$$ is not removable? \(\begin{array}{ll}{(\mathbf{A}) x=-1} & {(\mathbf{B}) x=0} \\ {(\mathbf{D}) x=2} & {(\mathbf{E}) x=3}\end{array} \quad(\mathbf{C}) x=1\)
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