Exam 1: Functions, Graphs, and Limits

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }$

At a certain factory, the total cost of manufacturing units during the daily production run is $C ( q ) = q ^ { 2 } + 2 q + 254$ dollars. On a typical day, q(t) = 16t units are manufactured during the first hours of a production run. How much is spent during the first 3 hours of production?

Find functions h(x) and g(u) such that $f ( x ) = g ( h ( x ) )$ : $f ( x ) = \sqrt [ 7 ] { 84 - 7 x - 4 x ^ { 2 } }$

List all the values of x for which the given function is not continuous. $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } & \text { if } x \leq 2 \\4 & \text { if } x > 2\end{aligned} \right.$

Find the slope (if possible) of the line that passes through the given pair of points. (11, 0) and (14, 11)

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ If the limiting value is infinite indicate whether it is + $\infty$ or - $\infty$ . $f ( x ) = \frac { 4 - 2 x ^ { 3 } } { 6 x ^ { 3 } - 6 x + 1 }$

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }$

Find the indicated composite function. f (x + 5) where $f ( x ) = \frac { 1 } { x }$

Find the slope and y-intercept of the line whose equation is given. $\frac { x } { 2 } + \frac { y } { 3 } = 1$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 2 } \frac { x - 2 } { x ^ { 2 } - 4 }$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }$

What is the slope of the line 7x + 8y = -3? Round your answer to two decimal places, if necessary.

Find the points of intersection (if any) of the given pair of curves. y = x + 2 and y = 2x + 4

List all the values of x for which the given function is not continuous. $f ( x ) = \left\{ \begin{array} { c l } x ^ { 3 } & \text { if } x \leq 5 \\125 & \text { if } x > 5\end{array} \right.$

A ball is thrown upward in such a way that t seconds later, it is $H ( t ) = - 16 t ^ { 2 } + 64 t + 80$ feet above the ground. How many seconds later does the ball hit the ground?

A closed cylindrical can has a surface area of 400 $\pi$ square inches. Express the volume of the can as a function of its radius, r.

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { 3 x ^ { 2 } - 5 x + 2 } { 2 x + 1 }$

Sketch the graph of the given function. $f ( x ) = x ^ { 2 } + 2$ (Tick marks are spaced one unit apart.)

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$

As a rumor spreads across a college campus, the number of people that have heard it can be modeled by the equation $N ( t ) = \frac { 6,200 t ^ { 2 } + 2,500 t } { ( t + 3 ) ^ { 2 } }$ where t is days since the rumor started spreading. What happens to the number of people that have heard the rumor in the long run (as $t \rightarrow \infty$ )?