Question 1

Calculate the following limit(s) if they exist.
-$\lim _ { x \rightarrow 2 }$ (2x + 2 $)^2$ Enter your answer as an integer, or "does not exist".

Accepted Answer

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

Question 2

Find the equation of the following line: Parallel to $6 x + y - 3 = 0$ ; (4, 3) on line.

Accepted Answer

A)  y = - $\frac { 1 } { 6 }$ x - $\frac { 9 } { 2 }$ 
B)  y = 6x - 27 
C)  y = - 6x - 27 
D)  y = - 6x + 27 
A)  y = - $\frac { 1 } { 6 }$ x - $\frac { 9 } { 2 }$ 
B)  y = 6x - 27 
C)  y = - 6x - 27 
D)  y = - 6x + 27

Question 3

Find the first derivative of y = $\mathrm{T}^{7}$ - 9 $\mathrm { T } ^ { 5 }$ + 2 $\mathrm { T } ^ { 4 }$ + 59

Accepted Answer

A)  $\mathrm { T } ^ { 6 }$ - 9 $\mathrm { T } ^ { 4 }$ + 2 $\mathrm { T } ^ { 3 }$ 
B)  $\mathrm { T } ^ { 6 }$ - 9 $\mathrm { T } ^ { 4 }$ + 2 $\mathrm { T } ^ { 3 }$ + 59 
C)  7 $\mathrm { T } ^ { 6 }$ - 45 $\mathrm { T } ^ { 4 }$ + 8 $\mathrm { T } ^ { 3 }$ + 59 
D)  7 $\mathrm { T } ^ { 6 }$ - 45 $\mathrm { T } ^ { 4 }$ + 8 $\mathrm { T } ^ { 3 }$ 
A)  $\mathrm { T } ^ { 6 }$ - 9 $\mathrm { T } ^ { 4 }$ + 2 $\mathrm { T } ^ { 3 }$ 
B)  $\mathrm { T } ^ { 6 }$ - 9 $\mathrm { T } ^ { 4 }$ + 2 $\mathrm { T } ^ { 3 }$ + 59 
C)  7 $\mathrm { T } ^ { 6 }$ - 45 $\mathrm { T } ^ { 4 }$ + 8 $\mathrm { T } ^ { 3 }$ + 59 
D)  7 $\mathrm { T } ^ { 6 }$ - 45 $\mathrm { T } ^ { 4 }$ + 8 $\mathrm { T } ^ { 3 }$

Question 4

Find the slope of the line with the equation y = 4 - 5x.
Enter just an integer.

Accepted Answer

The answer of Find the slope of the line with...

Question 5

For the following function g(x), determine whether or not $\lim _ { x \rightarrow 2 }$ g(x) exists. If so, give the limit.

Accepted Answer

A)  2 
B)  -6 
C)  0 
D)  does not exist 
A)  2 
B)  -6 
C)  0 
D)  does not exist

Question 6

Compute $$\frac { \mathrm { d } } { \mathrm { dt } }$$ $\left( \frac { \mathrm { dv } } { \mathrm { dt } } \right)$ , where v = -5 $t ^ { 3 }$ + $\frac { 2 } { 1 - t }$ at t = -1.
Enter just a reduced fraction of form $\frac { a } { b }$ .

Accepted Answer

The answer of Compute \[\frac { \mathrm { d }...

Question 7

Find the slope of the graph of f(x) = 1 + 3x - $x ^ { 2 }$ at x = 5.
Enter just an integer.

Accepted Answer

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

Question 8

A rock is thrown off a cliff. Its distance from the ground below at t seconds is $s ( t ) = - 16 t ^ { 2 } + 16 t + 96$ feet. When will it hit the ground?
Enter your answer exactly as: t = a. No units.

Accepted Answer

The answer of A rock is thrown off a cliff....

Question 9

Differentiate.
-f(x) = 4 $x ^ { 2 }$ - 5x + 7

Accepted Answer

A)  f'(x) = 4x - 5 
B)  f'(x) = 8x - 5 
C)  $f ^ { \prime } ( x ) = 8 { x ^ { 2 } } - 5$ 
D)  f'(x) = 4 $x ^ { 2 }$ - 5 
A)  f'(x) = 4x - 5 
B)  f'(x) = 8x - 5 
C)  $f ^ { \prime } ( x ) = 8 { x ^ { 2 } } - 5$ 
D)  f'(x) = 4 $x ^ { 2 }$ - 5

Question 10

Let f(x) = $\frac { 1 } { 2 x }$ . Compute $f ^ { \prime }$ (3) using limits.
Enter a reduced fraction or an integer.

Accepted Answer

The answer of Let f(x) = \(\frac { 1 }...

Question 11

Find second derivative of y = $x ^ { 3 / 2 }$ + $x ^ { 2 }$ at x = 4.
Enter just a fraction of form $\frac { a } { b }$ in lowest terms.

Accepted Answer

The answer of Find second derivative of y = \(x...

Question 12

If the cost function for producing a product is $C ( x ) = x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + 3 x + 2$ find the answer closest to the marginal cost at a production level of 10 units.

Accepted Answer

A)  -697 
B)  30 
C)  293 
D)  297 
E)  697 
A)  -697 
B)  30 
C)  293 
D)  297 
E)  697

Question 13

In the graph of y = f (x), for which values of x is f(x) not differentiable?
Enter your answer exactly in the form: x = a, b, c where a < b < c. (If there are fewer or more terms, separate them with commas in increasing order.)

Accepted Answer

The answer of In the graph of y = f...

Question 14

Find the equation of the following line: Perpendicular to 5x = 7 - 8y; y-intercept is -2.
Enter your answer in slope-intercept form with any fractions in the form $\frac { a } { b }$ in lowest terms.

Accepted Answer

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

Question 15

Differentiate.
-f(x) = $\frac { 2 x - \left( x ^ { 2 } + 1 \right) ^ { 7 } } { 3 }$

Accepted Answer

A)  f'(x) = $f ^ { \prime } ( x ) = 2 - 7 \left( x ^ { 2 } + 1 \right) ^ { 6 }$ 
B)  f'(x) = $\frac { 2 } { 3 }$ - $\frac { 14 } { 3 }$ x( $x ^ { 2 }$ + 1 $)^6$ 
C)  f'(x) = $\frac { 2 - x } { 3 \left( x ^ { 2 } + 1 \right) ^ { 6 } }$ 
D)  none of these 
A)  f'(x) = $f ^ { \prime } ( x ) = 2 - 7 \left( x ^ { 2 } + 1 \right) ^ { 6 }$ 
B)  f'(x) = $\frac { 2 } { 3 }$ - $\frac { 14 } { 3 }$ x( $x ^ { 2 }$ + 1 $)^6$ 
C)  f'(x) = $\frac { 2 - x } { 3 \left( x ^ { 2 } + 1 \right) ^ { 6 } }$ 
D)  none of these

Question 16

A rock is thrown off a cliff. Its distance from the ground below at t seconds is $s ( t ) = - 16 t ^ { 2 } + 16 t + 96$ feet. What is the velocity after 1 second?
Enter just an integer. No units.

Accepted Answer

The answer of A rock is thrown off a cliff....

Question 17

Calculate the following limit(s) if they exist.
-$\lim _ { x \rightarrow 3 }$ 4 $x ^ { 3 }$ Enter your answer as an integer.

Accepted Answer

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

Question 18

A manufacturer's profit from producing x units of a product is given by $P ( x ) = 0.002 x ^ { 3 } - 0.01 x ^ { 2 } + 0.5 x$ At what production level(s) will the marginal profit be $9.30 per unit?
Enter just an integer, no units.

Accepted Answer

The answer of A manufacturer's profit from producing x units...

Question 19

Write the word or phrase that best completes each statement or answers the question. 
-y = $\frac { 1 } { x ^ { 2 } + 1 }$ Enter your answer exactly in the form: $\frac { \mathrm { P } ( \mathrm { x } ) } { ( \mathrm { Q } ( \mathrm { x } ) ) ^ { \mathrm { a } } }$ where P(x) and Q(x) are polynomials in standard form.

Accepted Answer

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

Question 20

If f(x) = -2 $x ^ { 2 }$ - 3x + 2, find $\frac { f ( x + h ) - f ( x ) } { h }$ where h ? 0.

Accepted Answer

A)  $\frac { - 2 x ^ { 2 } - 2 h ^ { 2 } - 3 h } { h }$ 
B)  $\frac { - 2 h ^ { 2 } - 3 h + 2 } { h }$ 
C)  -4x - 2h - 3 
D)  -4x - 1 
E)  none of these 
A)  $\frac { - 2 x ^ { 2 } - 2 h ^ { 2 } - 3 h } { h }$ 
B)  $\frac { - 2 h ^ { 2 } - 3 h + 2 } { h }$ 
C)  -4x - 2h - 3 
D)  -4x - 1 
E)  none of these

Calculate the following limit(s) if they exist. - $\lim _ { x \rightarrow 2 }$ (2x + 2 $)^2$ Enter your answer as an integer, or "does not exist".

Find the equation of the following line: Parallel to $6 x + y - 3 = 0$ ; (4, 3) on line.

Find the first derivative of y = $\mathrm{T}^{7}$ - 9 $\mathrm { T } ^ { 5 }$ + 2 $\mathrm { T } ^ { 4 }$ + 59

Find the slope of the line with the equation y = 4 - 5x. Enter just an integer.

For the following function g(x), determine whether or not $\lim _ { x \rightarrow 2 }$ g(x) exists. If so, give the limit. $For the following function g(x), determine whether or not \lim _ { x \rightarrow 2 } g(x) exists. If so, give the limit.$

Compute $\frac { \mathrm { d } } { \mathrm { dt } }$ $\left( \frac { \mathrm { dv } } { \mathrm { dt } } \right)$ , where v = -5 $t ^ { 3 }$ + $\frac { 2 } { 1 - t }$ at t = -1. Enter just a reduced fraction of form $\frac { a } { b }$ .

Find the slope of the graph of f(x) = 1 + 3x - $x ^ { 2 }$ at x = 5. Enter just an integer.

A rock is thrown off a cliff. Its distance from the ground below at t seconds is $s ( t ) = - 16 t ^ { 2 } + 16 t + 96$ feet. When will it hit the ground? Enter your answer exactly as: t = a. No units.

Differentiate. -f(x) = 4 $x ^ { 2 }$ - 5x + 7

Let f(x) = $\frac { 1 } { 2 x }$ . Compute $f ^ { \prime }$ (3) using limits. Enter a reduced fraction or an integer.

Find second derivative of y = $x ^ { 3 / 2 }$ + $x ^ { 2 }$ at x = 4. Enter just a fraction of form $\frac { a } { b }$ in lowest terms.

If the cost function for producing a product is $C ( x ) = x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + 3 x + 2$ find the answer closest to the marginal cost at a production level of 10 units.

In the graph of y = f (x), for which values of x is f(x) not differentiable? Enter your answer exactly in the form: x = a, b, c where a < b < c. (If there are fewer or more terms, separate them with commas in increasing order.)

Find the equation of the following line: Perpendicular to 5x = 7 - 8y; y-intercept is -2. Enter your answer in slope-intercept form with any fractions in the form $\frac { a } { b }$ in lowest terms.

Differentiate. -f(x) = $\frac { 2 x - \left( x ^ { 2 } + 1 \right) ^ { 7 } } { 3 }$

A rock is thrown off a cliff. Its distance from the ground below at t seconds is $s ( t ) = - 16 t ^ { 2 } + 16 t + 96$ feet. What is the velocity after 1 second? Enter just an integer. No units.

Calculate the following limit(s) if they exist. - $\lim _ { x \rightarrow 3 }$ 4 $x ^ { 3 }$ Enter your answer as an integer.

A manufacturer's profit from producing x units of a product is given by $P ( x ) = 0.002 x ^ { 3 } - 0.01 x ^ { 2 } + 0.5 x$ At what production level(s) will the marginal profit be $9.30 per unit? Enter just an integer, no units.

If f(x) = -2 $x ^ { 2 }$ - 3x + 2, find $\frac { f ( x + h ) - f ( x ) } { h }$ where h ? 0.

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

Calculate the following limit(s) if they exist. - lim⁡x→2\lim _ { x \rightarrow 2 }limx→2​ (2x + 2 )2)^2)2 Enter your answer as an integer, or "does not exist".

Find the equation of the following line: Parallel to 6x+y−3=06 x + y - 3 = 06x+y−3=0 ; (4, 3) on line.

Find the first derivative of y = T7\mathrm{T}^{7}T7 - 9 T5\mathrm { T } ^ { 5 }T5 + 2 T4\mathrm { T } ^ { 4 }T4 + 59

Find the slope of the line with the equation y = 4 - 5x. Enter just an integer.

For the following function g(x), determine whether or not lim⁡x→2\lim _ { x \rightarrow 2 }limx→2​ g(x) exists. If so, give the limit.

Compute ddt\frac { \mathrm { d } } { \mathrm { dt } }dtd​ (dvdt)\left( \frac { \mathrm { dv } } { \mathrm { dt } } \right)(dtdv​) , where v = -5 t3t ^ { 3 }t3 + 21−t\frac { 2 } { 1 - t }1−t2​ at t = -1. Enter just a reduced fraction of form ab\frac { a } { b }ba​ .

Find the slope of the graph of f(x) = 1 + 3x - x2x ^ { 2 }x2 at x = 5. Enter just an integer.

A rock is thrown off a cliff. Its distance from the ground below at t seconds is s(t)=−16t2+16t+96s ( t ) = - 16 t ^ { 2 } + 16 t + 96s(t)=−16t2+16t+96 feet. When will it hit the ground? Enter your answer exactly as: t = a. No units.

Differentiate. -f(x) = 4 x2x ^ { 2 }x2 - 5x + 7

Let f(x) = 12x\frac { 1 } { 2 x }2x1​ . Compute f′f ^ { \prime }f′ (3) using limits. Enter a reduced fraction or an integer.

Find second derivative of y = x3/2x ^ { 3 / 2 }x3/2 + x2x ^ { 2 }x2 at x = 4. Enter just a fraction of form ab\frac { a } { b }ba​ in lowest terms.

If the cost function for producing a product is C(x)=x3−12x2+3x+2C ( x ) = x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + 3 x + 2C(x)=x3−2x21​+3x+2 find the answer closest to the marginal cost at a production level of 10 units.

In the graph of y = f (x), for which values of x is f(x) not differentiable? Enter your answer exactly in the form: x = a, b, c where a < b < c. (If there are fewer or more terms, separate them with commas in increasing order.)

Find the equation of the following line: Perpendicular to 5x = 7 - 8y; y-intercept is -2. Enter your answer in slope-intercept form with any fractions in the form ab\frac { a } { b }ba​ in lowest terms.

Differentiate. -f(x) = 2x−(x2+1)73\frac { 2 x - \left( x ^ { 2 } + 1 \right) ^ { 7 } } { 3 }32x−(x2+1)7​

A rock is thrown off a cliff. Its distance from the ground below at t seconds is s(t)=−16t2+16t+96s ( t ) = - 16 t ^ { 2 } + 16 t + 96s(t)=−16t2+16t+96 feet. What is the velocity after 1 second? Enter just an integer. No units.

Calculate the following limit(s) if they exist. - lim⁡x→3\lim _ { x \rightarrow 3 }limx→3​ 4 x3x ^ { 3 }x3 Enter your answer as an integer.

A manufacturer's profit from producing x units of a product is given by P(x)=0.002x3−0.01x2+0.5xP ( x ) = 0.002 x ^ { 3 } - 0.01 x ^ { 2 } + 0.5 xP(x)=0.002x3−0.01x2+0.5x At what production level(s) will the marginal profit be $9.30 per unit? Enter just an integer, no units.

If f(x) = -2 x2x ^ { 2 }x2 - 3x + 2, find f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ where h ? 0.

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

Calculate the following limit(s) if they exist. - $\lim _ { x \rightarrow 2 }$ (2x + 2 $)^2$ Enter your answer as an integer, or "does not exist".

Find the equation of the following line: Parallel to $6 x + y - 3 = 0$ ; (4, 3) on line.

Find the first derivative of y = $\mathrm{T}^{7}$ - 9 $\mathrm { T } ^ { 5 }$ + 2 $\mathrm { T } ^ { 4 }$ + 59

For the following function g(x), determine whether or not $\lim _ { x \rightarrow 2 }$ g(x) exists. If so, give the limit. $For the following function g(x), determine whether or not \lim _ { x \rightarrow 2 } g(x) exists. If so, give the limit.$

Compute $\frac { \mathrm { d } } { \mathrm { dt } }$ $\left( \frac { \mathrm { dv } } { \mathrm { dt } } \right)$ , where v = -5 $t ^ { 3 }$ + $\frac { 2 } { 1 - t }$ at t = -1. Enter just a reduced fraction of form $\frac { a } { b }$ .

Find the slope of the graph of f(x) = 1 + 3x - $x ^ { 2 }$ at x = 5. Enter just an integer.

A rock is thrown off a cliff. Its distance from the ground below at t seconds is $s ( t ) = - 16 t ^ { 2 } + 16 t + 96$ feet. When will it hit the ground? Enter your answer exactly as: t = a. No units.

Differentiate. -f(x) = 4 $x ^ { 2 }$ - 5x + 7

Let f(x) = $\frac { 1 } { 2 x }$ . Compute $f ^ { \prime }$ (3) using limits. Enter a reduced fraction or an integer.

Find second derivative of y = $x ^ { 3 / 2 }$ + $x ^ { 2 }$ at x = 4. Enter just a fraction of form $\frac { a } { b }$ in lowest terms.

If the cost function for producing a product is $C ( x ) = x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + 3 x + 2$ find the answer closest to the marginal cost at a production level of 10 units.

Find the equation of the following line: Perpendicular to 5x = 7 - 8y; y-intercept is -2. Enter your answer in slope-intercept form with any fractions in the form $\frac { a } { b }$ in lowest terms.

Differentiate. -f(x) = $\frac { 2 x - \left( x ^ { 2 } + 1 \right) ^ { 7 } } { 3 }$

A rock is thrown off a cliff. Its distance from the ground below at t seconds is $s ( t ) = - 16 t ^ { 2 } + 16 t + 96$ feet. What is the velocity after 1 second? Enter just an integer. No units.

Calculate the following limit(s) if they exist. - $\lim _ { x \rightarrow 3 }$ 4 $x ^ { 3 }$ Enter your answer as an integer.

A manufacturer's profit from producing x units of a product is given by $P ( x ) = 0.002 x ^ { 3 } - 0.01 x ^ { 2 } + 0.5 x$ At what production level(s) will the marginal profit be $9.30 per unit? Enter just an integer, no units.

If f(x) = -2 $x ^ { 2 }$ - 3x + 2, find $\frac { f ( x + h ) - f ( x ) } { h }$ where h ? 0.