Question 1

A farmer is planning to plant a rectangular garden with an area of 400 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

Accepted Answer

The answer of A farmer is planning to plant a...

Question 2

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +$\infty$ or -$\infty$. $$\lim _ { x \rightarrow 2 ^ { + } } f ( x )$$ where $$f ( x ) = \left\{ \begin{array} { c c } 
x ^ { 2 } & \text { if } x \leq 2 \
x + 1 & \text { if } x > 2
\end{array} \right.$$

Accepted Answer

The answer of Find the indicated one-sided limit. If the...

Question 3

A closed box with a square base is to have a volume of 40 cubic meters. The material for the top and bottom of the box costs $2 per square meter, and the material for the sides costs $4 per square meter. Express the construction cost of the box as a function of the length of its base, x.

Accepted Answer

The answer of A closed box with a square base...

Question 4

Plot the given point in a rectangular coordinate system.(-3, 1)

Accepted Answer

The answer of Plot the given point in a rectangular...

Question 5

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +$\infty$ or -$\infty$. $$\lim _ { x \rightarrow 2 ^ { - } } f ( x )$$ where $$f ( x ) = \left\{ \begin{array} { c c } 
x ^ { 2 } & \text { if } x \leq 2 \
x + 1 & \text { if } x > 2
\end{array} \right.$$

Accepted Answer

The answer of Find the indicated one-sided limit. If the...

Question 6

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

Accepted Answer

The answer of Find the indicated limit if it exists....

Question 7

Find the indicated composite function. f (4x - 5) where $f ( x ) = \frac { 1 } { x } - x$

Accepted Answer

The answer of Find the indicated composite function. f (4x...

Question 8

A ball is thrown upward in such a way that t seconds later it is $H ( t ) = - 11 t ^ { 2 } + 44 t + 55$ feet above the ground. When does the ball hit the ground?

Accepted Answer

The answer of A ball is thrown upward in such...

Question 9

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 -$\infty$. $f ( x ) = \frac { 5 - 3 x ^ { 3 } } { 7 x ^ { 3 } - x - 2 }$

Accepted Answer

The answer of Find \(\lim _ { x \rightarrow +...

Question 10

List all values of x for which f (x) is not continuous. $$f ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }$$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  -1 
C)  None 
D)  0 and -1

Question 11

A manufacturer's total cost consists of a fixed overhead of $250 plus production costs of $70 per unit. Express the total cost in dollars as a function of the number of units produced.

Accepted Answer

The answer of A manufacturer's total cost consists of a...

Question 12

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) = (5 - 9x)(x - 2)

Accepted Answer

A)  -$\infty$,-$\infty$ 
B)  -$\infty$,0 
C)  +$\infty$,+$\infty$. 
D)  +$\infty$,0

Question 13

Find the distance between the given points. (-2, 1) and (7, -5)

Accepted Answer

A)  $D = \sqrt { 15 }$ 
B)  D = 15 
C)  D = 117 
D)  $D = 3 \sqrt { 13 }$

Question 14

To study the rate at which animals learn, a psychology student performed an experiment in which a rat was sent repeatedly through a laboratory maze. Suppose the time required for the rat to traverse the maze on the $n ^ { t h }$ trial was approximately $T ( n ) = 8 + \frac { 4 } { n } - \frac { 8 } { n ^ { 2 } }$ minutes. How long does it take the rat to traverse the maze in the second trial?

Accepted Answer

The answer of To study the rate at which animals...

Question 15

A cylindrical can is to have a volume of 45 $\pi$ cubic inches. The cost of the material used for the top and bottom of the can is 4 cents per square inch, and the cost of the material used for the curved side is 5 cents per square inch. Express the cost of constructing the can as a function of its radius.

Accepted Answer

The answer of A cylindrical can is to have a...

Question 16

A ball is thrown upward in such a way that t seconds later, it is $s = - 16 t ^ { 2 } + 96 t + 144$ feet above the ground. Sketch the graph of s(t) and determine the maximum height in feet attained by the ball.

Accepted Answer

The answer of A ball is thrown upward in such...

Question 17

Compute the indicated value of the given function. f (x) = | x - 3 | + x - 5; f (2)

Accepted Answer

A)  -4 
B)  2 
C)  -2 
D)  1

Question 18

Determine the domain of the given function. $$f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 3 x + 1$$

Accepted Answer

A)  all real numbers x 
B)  all real numbers x except x = 1 
C)  all real numbers x except x = -1 
D)  all real numbers x except x = 0

Question 19

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +$\infty$ or -$\infty$. $\lim _ { x \rightarrow 5^- } f ( x )$ where $f ( x ) = \left\{ \begin{array} { c l } 
x ^ { 2 } & \text { if } x \leq 5 \
x + 1 & \text { if } x > 5
\end{array} \right.$

Accepted Answer

The answer of Find the indicated one-sided limit. If the...

Question 20

As a rumor spreads across a college campus, the number of people that have heard it can be modeled by the equation $N ( t ) = \frac { 7,600 t ^ { 2 } + 3,800 t } { ( t + 3 ) ^ { 2 } }$ 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 $t \rightarrow \infty$ )?

Accepted Answer

The answer of As a rumor spreads across a college...

Exam 1: Functions, Graphs, and Limits

A farmer is planning to plant a rectangular garden with an area of 400 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 2 ^ { + } } f ( x )$ where $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & \text { if } x \leq 2 \\x + 1 & \text { if } x > 2\end{array} \right.$

A closed box with a square base is to have a volume of 40 cubic meters. The material for the top and bottom of the box costs $2 per square meter, and the material for the sides costs $4 per square meter. Express the construction cost of the box as a function of the length of its base, x.

Plot the given point in a rectangular coordinate system.(-3, 1)

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 2 ^ { - } } f ( x )$ where $f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & \text { if } x \leq 2 \\x + 1 & \text { if } x > 2\end{array} \right.$

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

Find the indicated composite function. f (4x - 5) where $f ( x ) = \frac { 1 } { x } - x$

A ball is thrown upward in such a way that t seconds later it is $H ( t ) = - 11 t ^ { 2 } + 44 t + 55$ feet above the ground. When does the ball hit the ground?

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 - $\infty$ . $f ( x ) = \frac { 5 - 3 x ^ { 3 } } { 7 x ^ { 3 } - x - 2 }$

List all values of x for which f (x) is not continuous. $f ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }$

A manufacturer's total cost consists of a fixed overhead of $250 plus production costs of $70 per unit. Express the total cost in dollars as a function of the number of units produced.

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) = (5 - 9x) (x - 2)

Find the distance between the given points. (-2, 1) and (7, -5)

A ball is thrown upward in such a way that t seconds later, it is $s = - 16 t ^ { 2 } + 96 t + 144$ feet above the ground. Sketch the graph of s(t) and determine the maximum height in feet attained by the ball.

Compute the indicated value of the given function. f (x) = | x - 3 | + x - 5; f (2)

Determine the domain of the given function. $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 3 x + 1$

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 5^- } f ( x )$ where $f ( x ) = \left\{ \begin{array} { c l } x ^ { 2 } & \text { if } x \leq 5 \\x + 1 & \text { if } x > 5\end{array} \right.$

Exam 1: Functions, Graphs, and Limits

A farmer is planning to plant a rectangular garden with an area of 400 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

A closed box with a square base is to have a volume of 40 cubic meters. The material for the top and bottom of the box costs $2 per square meter, and the material for the sides costs $4 per square meter. Express the construction cost of the box as a function of the length of its base, x.

Plot the given point in a rectangular coordinate system.(-3, 1)

Find the indicated limit if it exists. lim⁡x→12x−1x+3\lim _ { x \rightarrow 1 } \frac { 2 x - 1 } { x + 3 }limx→1​x+32x−1​

Find the indicated composite function. f (4x - 5) where f(x)=1x−xf ( x ) = \frac { 1 } { x } - xf(x)=x1​−x

A ball is thrown upward in such a way that t seconds later it is H(t)=−11t2+44t+55H ( t ) = - 11 t ^ { 2 } + 44 t + 55H(t)=−11t2+44t+55 feet above the ground. When does the ball hit the ground?

List all values of x for which f (x) is not continuous. f(x) =2x+1x2+xf ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }f(x) =x2+x2x+1​

A manufacturer's total cost consists of a fixed overhead of $250 plus production costs of $70 per unit. Express the total cost in dollars as a function of the number of units produced.

Find lim⁡x→+∞f(x) \lim _ { x \rightarrow + \infty } f ( x ) limx→+∞​f(x) and lim⁡x→−∞f(x) \lim _ { x \rightarrow - \infty } f ( x ) limx→−∞​f(x) . If the limiting value is infinite indicate whether it is + ∞\infty∞ or - ∞\infty∞ .f (x) = (5 - 9x) (x - 2)

Find the distance between the given points. (-2, 1) and (7, -5)

A ball is thrown upward in such a way that t seconds later, it is s=−16t2+96t+144s = - 16 t ^ { 2 } + 96 t + 144s=−16t2+96t+144 feet above the ground. Sketch the graph of s(t) and determine the maximum height in feet attained by the ball.

Compute the indicated value of the given function. f (x) = | x - 3 | + x - 5; f (2)

Determine the domain of the given function. f(x) =x4+2x3+3x+1f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 3 x + 1f(x) =x4+2x3+3x+1

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

Find the indicated composite function. f (4x - 5) where $f ( x ) = \frac { 1 } { x } - x$

A ball is thrown upward in such a way that t seconds later it is $H ( t ) = - 11 t ^ { 2 } + 44 t + 55$ feet above the ground. When does the ball hit the ground?

List all values of x for which f (x) is not continuous. $f ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }$

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) = (5 - 9x) (x - 2)

A ball is thrown upward in such a way that t seconds later, it is $s = - 16 t ^ { 2 } + 96 t + 144$ feet above the ground. Sketch the graph of s(t) and determine the maximum height in feet attained by the ball.

Determine the domain of the given function. $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 3 x + 1$