Question 1

Calculate the average rate of change of the given function over the interval $[ 1,3 ]$ . $$\begin{array} { | l | l | l | l | l | } 
\hline \boldsymbol { x } & 0 & 1 & 2 & 3 \
\hline f ( x ) & 5 & 1 & 1 & - 13 \
\hline
\end{array}$$ ​
​

Accepted Answer

-7

Question 2

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.   $f ( x ) = \frac { | x | } { 4 x } + 4$

Accepted Answer

A) The point of discontinuity: 4. 
B)  The points of discontinuity: $\frac { 1 } { 4 }$ , 0. 
C)  The points of discontinuity: 4, 0. 
D)  The function is continuous on its domain. 
E)  The point of discontinuity: 0. 
A) The point of discontinuity: 4. 
B)  The points of discontinuity: $\frac { 1 } { 4 }$ , 0. 
C)  The points of discontinuity: 4, 0. 
D)  The function is continuous on its domain. 
E)  The point of discontinuity: 0. D

Question 3

If $D ( t )$ is the Dow Jones Average at time  t and $\lim_ { t \rightarrow + \infty } D ( t ) = + \infty$ , is it possible that the Dow will fluctuate indefinitely into the future

Accepted Answer

A) yes 
B)  no 
A) yes 
B)  no A

Question 4

The chart shows the total annual support for the arts in the U.S. by federal, state, and local government in 1995-2003 as a function of time in years ( $$t = 0$$ represents 1995) together with the regression line.      
Over the period $[ 0,4 ]$ the average rate of change of government funding for the arts was _____ the rate predicted by the regression line.

Accepted Answer

A) greater than 
B)  less than 
C)  equal to 
A) greater than 
B)  less than 
C)  equal to

Question 5

Compute $f ^ { \prime } ( - 3.2 )$ .
​ $f ( x ) = 5.9 x + 9.3$

Accepted Answer

The answer of Compute \(f ^ { \prime } (...

Question 6

Estimate the limit numerically.   $\lim _ { x \rightarrow 13 } e ^ { x - 13 }$

Accepted Answer

A) 1 
B)  $- \infty$ 
C)   13 
D)  $+ \infty$ 
E)  0 
A) 1 
B)  $- \infty$ 
C)   13 
D)  $+ \infty$ 
E)  0

Question 7

The function $R ( t ) = 1,120 + 79 t - t ^ { 3 }$ represents the value of the U.S. dollar in Indian rupees as a function of the time t in days. Find the average rates of change of $R ( t )$ over the time intervals $[ t , t + h ]$ , where t is as indicated and $h = 1$ , $0.1$ , $0.01$ , and $0.0001$ days. Hence, estimate (using $h = 0.0001$ ) the instantaneous rate of change of $\text { R }$ at time $t = 2$ .  
Select your answer rounded to the nearest whole number.

Accepted Answer

A) 63 
B)  69 
C)  64 
D)  67 
E)  68 
A) 63 
B)  69 
C)  64 
D)  67 
E)  68

Question 8

The function given below gives the cost to manufacture x items. Estimate (using $h = 0.0001$ ) the instantaneous rate of change of the cost at the production level $x = 500$ .
​ $C ( x ) = 9,500 + 5 x - \frac { x ^ { 2 } } { 10,000 }$ ​
Enter your answer as a number without the units rounded to the nearest tenth.

Accepted Answer

The answer of The function given below gives the cost...

Question 9

Calculate the average rate of change of the given function over the interval $[ 7,8 ]$ .   $f ( x ) = \frac { x ^ { 2 } } { 7 } + \frac { 15 } { x }$

Accepted Answer

A)  $2 \frac { 7 } { 8 }$ 
B)  $\frac { 8 } { 15 }$ 
C)  $2 \frac { 1 } { 8 }$ 
D)  $1 \frac { 7 } { 8 }$ 
E)  $\frac { 7 } { 8 }$ 
A)  $2 \frac { 7 } { 8 }$ 
B)  $\frac { 8 } { 15 }$ 
C)  $2 \frac { 1 } { 8 }$ 
D)  $1 \frac { 7 } { 8 }$ 
E)  $\frac { 7 } { 8 }$

Question 10

Match each function with the corresponding graph.

Accepted Answer

A)  $f ( x ) = 3 x$ , $( - 3 \leq x \leq 3 )$ 
B)  $f ( x ) = - 3 x$ , $( - 3 \leq x \leq 3 )$ 
C)  $f ( x ) = | 3 x |$ , $( - 3 \leq x \leq 3 )$   
A)  $f ( x ) = 3 x$ , $( - 3 \leq x \leq 3 )$ 
B)  $f ( x ) = - 3 x$ , $( - 3 \leq x \leq 3 )$ 
C)  $f ( x ) = | 3 x |$ , $( - 3 \leq x \leq 3 )$

Question 11

Compute $f ^ { \prime } ( a )$ algebraically for $a = - 4$ .  
  $f ( x ) = 8 x + 8$

Accepted Answer

A)   $f ^ { \prime } ( - 4 ) = 8$ 
B)    $f ^ { \prime } ( - 4 ) = - 8$ 
C)    $f ^ { \prime } ( - 4 ) = 24$ 
D)    $f ^ { \prime } ( - 4 ) = 0$ 
E)    $f ^ { \prime } ( - 4 ) = 16$ 
A)   $f ^ { \prime } ( - 4 ) = 8$ 
B)    $f ^ { \prime } ( - 4 ) = - 8$ 
C)    $f ^ { \prime } ( - 4 ) = 24$ 
D)    $f ^ { \prime } ( - 4 ) = 0$ 
E)    $f ^ { \prime } ( - 4 ) = 16$

Question 12

Compute $f ^ { \prime } ( - 2.9 )$ .  
  $f ( x ) = 4.4 x + 5.9$

Accepted Answer

A)   $f ^ { \prime } ( - 2.9 ) = - 1.5$ 
B)    $f ^ { \prime } ( - 2.9 ) = - 7.4$ 
C)    $f ^ { \prime } ( - 2.9 ) = 16.2$ 
D)    $f ^ { \prime } ( - 2.9 ) = 4.4$ 
E)    $f ^ { \prime } ( - 2.9 ) = 10.3$ 
A)   $f ^ { \prime } ( - 2.9 ) = - 1.5$ 
B)    $f ^ { \prime } ( - 2.9 ) = - 7.4$ 
C)    $f ^ { \prime } ( - 2.9 ) = 16.2$ 
D)    $f ^ { \prime } ( - 2.9 ) = 4.4$ 
E)    $f ^ { \prime } ( - 2.9 ) = 10.3$

Question 13

Use the graph to compute $\lim_ { t \rightarrow -2 } f ( x )$ .
​

Accepted Answer

The answer of Use the graph to compute \(\lim_ {...

Question 14

Calculate the limit algebraically.  
  $\lim _ { x \rightarrow 4 } ( x + \sqrt { x } )$

Accepted Answer

A) 6 
B)  2 
C)  4 
D)  -2 
E)  8 
A) 6 
B)  2 
C)  4 
D)  -2 
E)  8

Question 15

Calculate the limit algebraically.
​ $\lim _ { x \rightarrow 0 } ( x + 3 )$ ​

Accepted Answer

The answer of Calculate the limit algebraically.
​ \(\lim _ {...

Question 16

Estimate the limit numerically.   $$\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } } { x + 4 }$$

Accepted Answer

A) 0 
B)  -4 
C)  diverges to $+ \infty$ 
D)  1 
E)  diverges to $- \infty$ 
A) 0 
B)  -4 
C)  diverges to $+ \infty$ 
D)  1 
E)  diverges to $- \infty$

Question 17

Compute $f ^ { \prime } ( 5 )$ .
​
​ $f ( x ) = \frac { 3.1 } { x }$ ​
Enter your answer rounded to the nearest thousandth.

Accepted Answer

The answer of Compute \(f ^ { \prime } (...

Question 18

For the slope 2.2, determine at which of the labeled points on the graph the tangent line has that slope. ​   ​

Accepted Answer

A) R 
B)  Q 
C)  P 
A) R 
B)  Q 
C)  P

Question 19

Compute $f ^ { \prime } ( 3 )$ .  
  $f ( x ) = 3.3 x ^ { 2 } + x$

Accepted Answer

A)   $f ^ { \prime } ( 3 ) = 32.7$ 
B)    $f ^ { \prime } ( 3 ) = 22.8$ 
C)    $f ^ { \prime } ( 3 ) = 20.8$ 
D)    $f ^ { \prime } ( 3 ) = 59.4$ 
E)    $f ^ { \prime } ( 3 ) = 62.4$ 
A)   $f ^ { \prime } ( 3 ) = 32.7$ 
B)    $f ^ { \prime } ( 3 ) = 22.8$ 
C)    $f ^ { \prime } ( 3 ) = 20.8$ 
D)    $f ^ { \prime } ( 3 ) = 59.4$ 
E)    $f ^ { \prime } ( 3 ) = 62.4$

Question 20

Calculate the limit algebraically.   $\lim _ { x \rightarrow 0 ^ { + } } \frac { 11 } { x ^ { 2 } - 6 x }$

Accepted Answer

A)  $\infty$ 
B)   11 
C)    $- \infty$ 
D)   -1.833 
E)    $0$ 
A)  $\infty$ 
B)   11 
C)    $- \infty$ 
D)   -1.833 
E)    $0$

Calculate the average rate of change of the given function over the interval $[ 1,3 ]$ . 0 1 2 3 f(x) 5 1 1 -13

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. $f ( x ) = \frac { | x | } { 4 x } + 4$

If $D ( t )$ is the Dow Jones Average at time t and $\lim_ { t \rightarrow + \infty } D ( t ) = + \infty$ , is it possible that the Dow will fluctuate indefinitely into the future

Compute $f ^ { \prime } ( - 3.2 )$ . $f ( x ) = 5.9 x + 9.3$

Estimate the limit numerically. $\lim _ { x \rightarrow 13 } e ^ { x - 13 }$

Calculate the average rate of change of the given function over the interval $[ 7,8 ]$ . $f ( x ) = \frac { x ^ { 2 } } { 7 } + \frac { 15 } { x }$

Match each function with the corresponding graph.

Compute $f ^ { \prime } ( a )$ algebraically for $a = - 4$ . $f ( x ) = 8 x + 8$

Compute $f ^ { \prime } ( - 2.9 )$ . $f ( x ) = 4.4 x + 5.9$

Use the graph to compute $\lim_ { t \rightarrow -2 } f ( x )$ . $Use the graph to compute \lim_ { t \rightarrow -2 } f ( x ) . $

Calculate the limit algebraically. $\lim _ { x \rightarrow 4 } ( x + \sqrt { x } )$

Calculate the limit algebraically. $\lim _ { x \rightarrow 0 } ( x + 3 )$

Estimate the limit numerically. $\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } } { x + 4 }$

Compute $f ^ { \prime } ( 5 )$ . $f ( x ) = \frac { 3.1 } { x }$ Enter your answer rounded to the nearest thousandth.

For the slope 2.2, determine at which of the labeled points on the graph the tangent line has that slope.

Compute $f ^ { \prime } ( 3 )$ . $f ( x ) = 3.3 x ^ { 2 } + x$

Calculate the limit algebraically. $\lim _ { x \rightarrow 0 ^ { + } } \frac { 11 } { x ^ { 2 } - 6 x }$

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

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Exam 10: Introduction to the Derivative

Calculate the average rate of change of the given function over the interval [1,3][ 1,3 ][1,3] . 0 1 2 3 f(x) 5 1 1 -13 ​ ​

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. f(x)=∣x∣4x+4f ( x ) = \frac { | x | } { 4 x } + 4f(x)=4x∣x∣​+4

If D(t)D ( t )D(t) is the Dow Jones Average at time t and lim⁡t→+∞D(t)=+∞\lim_ { t \rightarrow + \infty } D ( t ) = + \inftylimt→+∞​D(t)=+∞ , is it possible that the Dow will fluctuate indefinitely into the future

Compute f′(−3.2)f ^ { \prime } ( - 3.2 )f′(−3.2) . ​ f(x)=5.9x+9.3f ( x ) = 5.9 x + 9.3f(x)=5.9x+9.3

Estimate the limit numerically. lim⁡x→13ex−13\lim _ { x \rightarrow 13 } e ^ { x - 13 }limx→13​ex−13

Calculate the average rate of change of the given function over the interval [7,8][ 7,8 ][7,8] . f(x)=x27+15xf ( x ) = \frac { x ^ { 2 } } { 7 } + \frac { 15 } { x }f(x)=7x2​+x15​

Match each function with the corresponding graph.

Compute f′(a)f ^ { \prime } ( a )f′(a) algebraically for a=−4a = - 4a=−4 . f(x)=8x+8f ( x ) = 8 x + 8f(x)=8x+8

Compute f′(−2.9)f ^ { \prime } ( - 2.9 )f′(−2.9) . f(x)=4.4x+5.9f ( x ) = 4.4 x + 5.9f(x)=4.4x+5.9

Use the graph to compute lim⁡t→−2f(x)\lim_ { t \rightarrow -2 } f ( x )limt→−2​f(x) . ​

Calculate the limit algebraically. lim⁡x→4(x+x)\lim _ { x \rightarrow 4 } ( x + \sqrt { x } )limx→4​(x+x​)

Calculate the limit algebraically. ​ lim⁡x→0(x+3)\lim _ { x \rightarrow 0 } ( x + 3 )limx→0​(x+3) ​

Estimate the limit numerically. lim⁡x→0x2x+4\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } } { x + 4 }limx→0​x+4x2​

Compute f′(5)f ^ { \prime } ( 5 )f′(5) . ​ ​ f(x)=3.1xf ( x ) = \frac { 3.1 } { x }f(x)=x3.1​ ​ Enter your answer rounded to the nearest thousandth.

For the slope 2.2, determine at which of the labeled points on the graph the tangent line has that slope. ​ ​

Compute f′(3)f ^ { \prime } ( 3 )f′(3) . f(x)=3.3x2+xf ( x ) = 3.3 x ^ { 2 } + xf(x)=3.3x2+x

Calculate the limit algebraically. lim⁡x→0+11x2−6x\lim _ { x \rightarrow 0 ^ { + } } \frac { 11 } { x ^ { 2 } - 6 x }limx→0+​x2−6x11​

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Calculate the average rate of change of the given function over the interval $[ 1,3 ]$ . 0 1 2 3 f(x) 5 1 1 -13

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. $f ( x ) = \frac { | x | } { 4 x } + 4$

If $D ( t )$ is the Dow Jones Average at time t and $\lim_ { t \rightarrow + \infty } D ( t ) = + \infty$ , is it possible that the Dow will fluctuate indefinitely into the future

Compute $f ^ { \prime } ( - 3.2 )$ . $f ( x ) = 5.9 x + 9.3$

Estimate the limit numerically. $\lim _ { x \rightarrow 13 } e ^ { x - 13 }$

Calculate the average rate of change of the given function over the interval $[ 7,8 ]$ . $f ( x ) = \frac { x ^ { 2 } } { 7 } + \frac { 15 } { x }$

Compute $f ^ { \prime } ( a )$ algebraically for $a = - 4$ . $f ( x ) = 8 x + 8$

Compute $f ^ { \prime } ( - 2.9 )$ . $f ( x ) = 4.4 x + 5.9$

Use the graph to compute $\lim_ { t \rightarrow -2 } f ( x )$ . $Use the graph to compute \lim_ { t \rightarrow -2 } f ( x ) . $

Calculate the limit algebraically. $\lim _ { x \rightarrow 4 } ( x + \sqrt { x } )$

Calculate the limit algebraically. $\lim _ { x \rightarrow 0 } ( x + 3 )$

Estimate the limit numerically. $\lim _ { x \rightarrow 0 } \frac { x ^ { 2 } } { x + 4 }$

Compute $f ^ { \prime } ( 5 )$ . $f ( x ) = \frac { 3.1 } { x }$ Enter your answer rounded to the nearest thousandth.

For the slope 2.2, determine at which of the labeled points on the graph the tangent line has that slope.

Compute $f ^ { \prime } ( 3 )$ . $f ( x ) = 3.3 x ^ { 2 } + x$

Calculate the limit algebraically. $\lim _ { x \rightarrow 0 ^ { + } } \frac { 11 } { x ^ { 2 } - 6 x }$