Question 1

Find the equation of the following line: Parallel to y = - $\frac { 1 } { 4 }$ x + 8; (4, 4) on line.

Accepted Answer

A)  y = - $\frac { 1 } { 4 }$ x + 5 
B)  y = - 4x - 20 
C)  y = $\frac { 1 } { 4 }$ x - 5 
D)  y = - $\frac { 1 } { 4 }$ x - 5 
A)  y = - $\frac { 1 } { 4 }$ x + 5 
B)  y = - 4x - 20 
C)  y = $\frac { 1 } { 4 }$ x - 5 
D)  y = - $\frac { 1 } { 4 }$ x - 5

Question 2

A winter storm front moves through campus. At t hours after the onset of the storm, the temperature is given by $T ( t ) = 35 - 2 t ^ { 2 } + t$ What is the temperature 3 hours after the storm begins?
Enter just an integer, no units.

Accepted Answer

The answer of A winter storm front moves through campus....

Question 3

Find the equation of the following line: (2, 3) and (4, 6) on line.
Enter your answer in slope-intercept form.
Include both the slope and the intercept in your equation.

Accepted Answer

The answer of Find the equation of the following line:...

Question 4

A winter storm front moves through campus. At t hours after the onset of the storm, the temperature is given by $T ( t ) = 35 - 2 t ^ { 2 } + t$ . At what rate is the temperature changing 3 hours after the storm begins? $\text { Enter just an integer, no unit }$

Accepted Answer

The answer of A winter storm front moves through campus....

Question 5

At time t = 0, a seed is planted. After t weeks, the height of the plant is given by $f ( t ) = 0.3 t ^ { 2 } + 0.6 t + 0.5$ inches. At what rate is the plant growing after 8 weeks?

Accepted Answer

A)  5.4 inches/week 
B)  10.1 inches/week 
C)  0.6t + 0.6 inches/week 
D)  24.5 inches/week 
E)  none of these 
A)  5.4 inches/week 
B)  10.1 inches/week 
C)  0.6t + 0.6 inches/week 
D)  24.5 inches/week 
E)  none of these

Question 6

Write the word or phrase that best completes each statement or answers the question. 
-y = $\sqrt { x ^ { 4 } + 1 }$ Enter your answer exactly as: $\frac { d y } { d x } = \frac { P ( x ) } { \sqrt { Q ( x ) } }$ where P(x) and Q(x) are polynomials in standard form.

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Write the word or phrase that best completes each statement or answers the question. 
-y = $\frac { 4 } { 3 x ^ { 3 } + x ^ { 2 } + 4 }$ Enter your answer as just: $\frac { \mathrm { P } ( \mathrm { x } ) } { ( \mathrm { Q } ( \mathrm { x } ) ) ^ { \mathrm { a } } }$ where P(x) and Q(x) are polynomials in standard form.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Find $\frac { \mathrm { d } } { \mathrm { du } }$ $\sqrt { u ^ { 4 } - 7 }$ .

Accepted Answer

A)  $\frac { 2 u ^ { 3 } } { \sqrt { u ^ { 4 } - 7 } }$ 
B)  $\frac { 2 u } { \sqrt { u ^ { 2 } - 7 } }$ 
C)  $\frac { 4 u } { \sqrt { u ^ { 2 } - 7 } }$ 
D)  $\frac { 2 u } { \sqrt { u ^ { 4 } - 7 } }$ 
A)  $\frac { 2 u ^ { 3 } } { \sqrt { u ^ { 4 } - 7 } }$ 
B)  $\frac { 2 u } { \sqrt { u ^ { 2 } - 7 } }$ 
C)  $\frac { 4 u } { \sqrt { u ^ { 2 } - 7 } }$ 
D)  $\frac { 2 u } { \sqrt { u ^ { 4 } - 7 } }$

Question 9

If (x,y) is a point on the parabola y = 3 $x ^ { 2 }$ , then the tangent line to y = 3 $x ^ { 2 }$ passing through (x,y) has slope 6x. Find the equation of the line tangent to y = 3 $x ^ { 2 }$ through the point (-2, 12).

Accepted Answer

A)  y = 6x + 12 
B)  y = 12x + 6 
C)  y = -12x - 12 
D)  y = -2x + 12 
A)  y = 6x + 12 
B)  y = 12x + 6 
C)  y = -12x - 12 
D)  y = -2x + 12

Question 10

What is the equation of the tangent line to the graph of y = $x ^ { 2 }$ at the point where $x = \frac { 1 } { 3 }$ ?
Enter your answer in standard point-slope form.

Accepted Answer

The answer of What is the equation of the tangent...

Question 11

Find the slope of the graph of y = $x^9$ - 2x + $( \sqrt { 5 - x } ) ^ { 3 }$ at (1, 7).
Enter just an integer.

Accepted Answer

The answer of Find the slope of the graph of...

Question 12

Calculate the following limit(s) if they exist.
-$\lim _ { x \rightarrow - 2 }$ $\frac { x } { \left( x ^ { 3 } + 8 \right) ^ { - 1 } }$ Enter either a fraction, integer, or the words "does not exist".

Accepted Answer

The answer of Calculate the following limit(s) if they exist.
-\(\lim...

Question 13

Write the word or phrase that best completes each statement or answers the question. 
-y = - $\frac { 1 } { 2 x ^ { 2 } }$ Enter your answer exactly in the form: a $x ^ { b }$ where a,b are fractions or integers. No parentheses. If a power or coefficient is "1" then leave it off.

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Find the second derivative of f(x) = 7 $x ^ { 2 }$ + 7x - 7

Accepted Answer

A)  14x + 7 
B)  0 
C)  14 
D)  7 
A)  14x + 7 
B)  0 
C)  14 
D)  7

Question 15

Let f(x) = $\frac { x ^ { 3 } - 9 x } { 2 x + 6 }$ . Is f(x) continuous at x = -3?

Accepted Answer

A) True 
 B)False

Question 16

Find the (instantaneous) velocity at time t = 2 seconds for a falling object where the height function is given by $h ( t ) = - 16 t ^ { 2 } + 60 t + 30$ in feet.

Accepted Answer

A)  86 feet/second 
B)  28 feet/second 
C)  -86 feet/second 
D)  4 feet/second 
E)  -4 feet/second 
A)  86 feet/second 
B)  28 feet/second 
C)  -86 feet/second 
D)  4 feet/second 
E)  -4 feet/second

Question 17

For the graphed function below, state the x-values for which the derivative does not exist.

Accepted Answer

A)  x = 4, - 4 
B)  x = 0, 2, - 2 
C)  x = 2, - 2 
D)  x = 0, 4, - 4 
A)  x = 4, - 4 
B)  x = 0, 2, - 2 
C)  x = 2, - 2 
D)  x = 0, 4, - 4

Question 18

Find the equation of the tangent line to the curve y = $\sqrt { x ^ { 2 } + 5 }$ at (2, 3).
Enter your answer in standard point-slope form using reduced fractions and integers.

Accepted Answer

The answer of Find the equation of the tangent line...

Question 19

Find the equation of the following line: Slope is - $\frac { 5 } { 7 }$ ; $\left( - \frac { 1 } { 2 } , 1 \right)$ on line.
Enter your answer in point-slope form.

Accepted Answer

The answer of Find the equation of the following line:...

Question 20

Find the average rate of change for $f ( x ) = - 3 x ^ { 2 } - 2 x + 5$ on [-2, 1]

Accepted Answer

A)  - 7 
B)  1 
C)  -3 
D)  0 
E)  3 
A)  - 7 
B)  1 
C)  -3 
D)  0 
E)  3

Find the equation of the following line: Parallel to y = - $\frac { 1 } { 4 }$ x + 8; (4, 4) on line.

A winter storm front moves through campus. At t hours after the onset of the storm, the temperature is given by $T ( t ) = 35 - 2 t ^ { 2 } + t$ What is the temperature 3 hours after the storm begins? Enter just an integer, no units.

Find the equation of the following line: (2, 3) and (4, 6) on line. Enter your answer in slope-intercept form. Include both the slope and the intercept in your equation.

A winter storm front moves through campus. At t hours after the onset of the storm, the temperature is given by $T ( t ) = 35 - 2 t ^ { 2 } + t$ . At what rate is the temperature changing 3 hours after the storm begins? $\text { Enter just an integer, no unit }$

At time t = 0, a seed is planted. After t weeks, the height of the plant is given by $f ( t ) = 0.3 t ^ { 2 } + 0.6 t + 0.5$ inches. At what rate is the plant growing after 8 weeks?

Write the word or phrase that best completes each statement or answers the question. -y = $\sqrt { x ^ { 4 } + 1 }$ Enter your answer exactly as: $\frac { d y } { d x } = \frac { P ( x ) } { \sqrt { Q ( x ) } }$ where P(x) and Q(x) are polynomials in standard form.

Find $\frac { \mathrm { d } } { \mathrm { du } }$ $\sqrt { u ^ { 4 } - 7 }$ .

If (x,y) is a point on the parabola y = 3 $x ^ { 2 }$ , then the tangent line to y = 3 $x ^ { 2 }$ passing through (x,y) has slope 6x. Find the equation of the line tangent to y = 3 $x ^ { 2 }$ through the point (-2, 12).

What is the equation of the tangent line to the graph of y = $x ^ { 2 }$ at the point where $x = \frac { 1 } { 3 }$ ? Enter your answer in standard point-slope form.

Find the slope of the graph of y = $x^9$ - 2x + $( \sqrt { 5 - x } ) ^ { 3 }$ at (1, 7). Enter just an integer.

Calculate the following limit(s) if they exist. - $\lim _ { x \rightarrow - 2 }$ $\frac { x } { \left( x ^ { 3 } + 8 \right) ^ { - 1 } }$ Enter either a fraction, integer, or the words "does not exist".

Write the word or phrase that best completes each statement or answers the question. -y = - $\frac { 1 } { 2 x ^ { 2 } }$ Enter your answer exactly in the form: a $x ^ { b }$ where a,b are fractions or integers. No parentheses. If a power or coefficient is "1" then leave it off.

Find the second derivative of f(x) = 7 $x ^ { 2 }$ + 7x - 7

Let f(x) = $\frac { x ^ { 3 } - 9 x } { 2 x + 6 }$ . Is f(x) continuous at x = -3?

Find the (instantaneous) velocity at time t = 2 seconds for a falling object where the height function is given by $h ( t ) = - 16 t ^ { 2 } + 60 t + 30$ in feet.

For the graphed function below, state the x-values for which the derivative does not exist.

Find the equation of the tangent line to the curve y = $\sqrt { x ^ { 2 } + 5 }$ at (2, 3). Enter your answer in standard point-slope form using reduced fractions and integers.

Find the equation of the following line: Slope is - $\frac { 5 } { 7 }$ ; $\left( - \frac { 1 } { 2 } , 1 \right)$ on line. Enter your answer in point-slope form.

Find the average rate of change for $f ( x ) = - 3 x ^ { 2 } - 2 x + 5$ on [-2, 1]

Applications of the Derivative

Techniques of Differentiation

Logarithm Functions

Applications of the Exponential and Natural Logarithm Functions

The Definite Integral

Functions of Several Variables

The Trigonometric Functions

Techniques of Integration

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Filters

Exam 1: The Derivative

Find the equation of the following line: Parallel to y = - 14\frac { 1 } { 4 }41​ x + 8; (4, 4) on line.

A winter storm front moves through campus. At t hours after the onset of the storm, the temperature is given by T(t)=35−2t2+tT ( t ) = 35 - 2 t ^ { 2 } + tT(t)=35−2t2+t What is the temperature 3 hours after the storm begins? Enter just an integer, no units.

Find the equation of the following line: (2, 3) and (4, 6) on line. Enter your answer in slope-intercept form. Include both the slope and the intercept in your equation.

At time t = 0, a seed is planted. After t weeks, the height of the plant is given by f(t)=0.3t2+0.6t+0.5f ( t ) = 0.3 t ^ { 2 } + 0.6 t + 0.5f(t)=0.3t2+0.6t+0.5 inches. At what rate is the plant growing after 8 weeks?

Find ddu\frac { \mathrm { d } } { \mathrm { du } }dud​ u4−7\sqrt { u ^ { 4 } - 7 }u4−7​ .

If (x,y) is a point on the parabola y = 3 x2x ^ { 2 }x2 , then the tangent line to y = 3 x2x ^ { 2 }x2 passing through (x,y) has slope 6x. Find the equation of the line tangent to y = 3 x2x ^ { 2 }x2 through the point (-2, 12).

What is the equation of the tangent line to the graph of y = x2x ^ { 2 }x2 at the point where x=13x = \frac { 1 } { 3 }x=31​ ? Enter your answer in standard point-slope form.

Find the slope of the graph of y = x9x^9x9 - 2x + (5−x)3( \sqrt { 5 - x } ) ^ { 3 }(5−x​)3 at (1, 7). Enter just an integer.

Calculate the following limit(s) if they exist. - lim⁡x→−2\lim _ { x \rightarrow - 2 }limx→−2​ x(x3+8)−1\frac { x } { \left( x ^ { 3 } + 8 \right) ^ { - 1 } }(x3+8)−1x​ Enter either a fraction, integer, or the words "does not exist".

Write the word or phrase that best completes each statement or answers the question. -y = - 12x2\frac { 1 } { 2 x ^ { 2 } }2x21​ Enter your answer exactly in the form: a xbx ^ { b }xb where a,b are fractions or integers. No parentheses. If a power or coefficient is "1" then leave it off.

Find the second derivative of f(x) = 7 x2x ^ { 2 }x2 + 7x - 7

Let f(x) = x3−9x2x+6\frac { x ^ { 3 } - 9 x } { 2 x + 6 }2x+6x3−9x​ . Is f(x) continuous at x = -3?

Find the (instantaneous) velocity at time t = 2 seconds for a falling object where the height function is given by h(t)=−16t2+60t+30h ( t ) = - 16 t ^ { 2 } + 60 t + 30h(t)=−16t2+60t+30 in feet.

For the graphed function below, state the x-values for which the derivative does not exist.

Find the equation of the tangent line to the curve y = x2+5\sqrt { x ^ { 2 } + 5 }x2+5​ at (2, 3). Enter your answer in standard point-slope form using reduced fractions and integers.

Find the equation of the following line: Slope is - 57\frac { 5 } { 7 }75​ ; (−12,1)\left( - \frac { 1 } { 2 } , 1 \right)(−21​,1) on line. Enter your answer in point-slope form.

Find the average rate of change for f(x)=−3x2−2x+5f ( x ) = - 3 x ^ { 2 } - 2 x + 5f(x)=−3x2−2x+5 on [-2, 1]

Applications of the Derivative

Techniques of Differentiation

Logarithm Functions

Applications of the Exponential and Natural Logarithm Functions

The Definite Integral

Functions of Several Variables

The Trigonometric Functions

Techniques of Integration

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Filters

Find the equation of the following line: Parallel to y = - $\frac { 1 } { 4 }$ x + 8; (4, 4) on line.

A winter storm front moves through campus. At t hours after the onset of the storm, the temperature is given by $T ( t ) = 35 - 2 t ^ { 2 } + t$ What is the temperature 3 hours after the storm begins? Enter just an integer, no units.

At time t = 0, a seed is planted. After t weeks, the height of the plant is given by $f ( t ) = 0.3 t ^ { 2 } + 0.6 t + 0.5$ inches. At what rate is the plant growing after 8 weeks?

Find $\frac { \mathrm { d } } { \mathrm { du } }$ $\sqrt { u ^ { 4 } - 7 }$ .

If (x,y) is a point on the parabola y = 3 $x ^ { 2 }$ , then the tangent line to y = 3 $x ^ { 2 }$ passing through (x,y) has slope 6x. Find the equation of the line tangent to y = 3 $x ^ { 2 }$ through the point (-2, 12).

What is the equation of the tangent line to the graph of y = $x ^ { 2 }$ at the point where $x = \frac { 1 } { 3 }$ ? Enter your answer in standard point-slope form.

Find the slope of the graph of y = $x^9$ - 2x + $( \sqrt { 5 - x } ) ^ { 3 }$ at (1, 7). Enter just an integer.

Calculate the following limit(s) if they exist. - $\lim _ { x \rightarrow - 2 }$ $\frac { x } { \left( x ^ { 3 } + 8 \right) ^ { - 1 } }$ Enter either a fraction, integer, or the words "does not exist".

Write the word or phrase that best completes each statement or answers the question. -y = - $\frac { 1 } { 2 x ^ { 2 } }$ Enter your answer exactly in the form: a $x ^ { b }$ where a,b are fractions or integers. No parentheses. If a power or coefficient is "1" then leave it off.

Find the second derivative of f(x) = 7 $x ^ { 2 }$ + 7x - 7

Let f(x) = $\frac { x ^ { 3 } - 9 x } { 2 x + 6 }$ . Is f(x) continuous at x = -3?

Find the (instantaneous) velocity at time t = 2 seconds for a falling object where the height function is given by $h ( t ) = - 16 t ^ { 2 } + 60 t + 30$ in feet.

Find the equation of the tangent line to the curve y = $\sqrt { x ^ { 2 } + 5 }$ at (2, 3). Enter your answer in standard point-slope form using reduced fractions and integers.

Find the equation of the following line: Slope is - $\frac { 5 } { 7 }$ ; $\left( - \frac { 1 } { 2 } , 1 \right)$ on line. Enter your answer in point-slope form.

Find the average rate of change for $f ( x ) = - 3 x ^ { 2 } - 2 x + 5$ on [-2, 1]