Exam 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -If an object is thrown straight upward from the ground with an initial speed of 112 feet per second, then its height, $h$ , in feet after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 112 t$ . Find the instantaneous speed of the object at $t = 6$

Use the grid to graph the function. Find the limit, if it exists - $\lim _ { x \rightarrow 8 } f ( x ) , \quad f ( x ) = 4 x - 1$

Write the word or phrase that best completes each statement or answers the question. - $f ( x ) = \tan x$ is defined over the interval $\left[ 0 , \frac { 3 } { 2 } \right]$ (a) Approximate the area A by partitioning $\left[ 0 , \frac { 3 } { 2 } \right]$ into 4 subintervals of equal length and choosing $u$ as the left endpoint of each subinterval. (b) Approximate the area A by partitioning $\left[ 0 , \frac { 3 } { 2 } \right]$ into 8 subintervals of equal length and choosing us the right endpoint of each subinterval. (c) Express the area A as an integral. (d) Use a graphing utility to approximate this integral to three decimal places.

Find the one-sided limit. - $\lim _ { x - ( 3 \pi / 4 ) ^ { - } } \sin x$

Determine whether f is continuous at c. - $f ( x ) = \frac { x - 6 } { ( x - 1 ) ( x - 9 ) } ; \quad c = 0$