Question 1

The volume of a cube is increasing at a rate of   . How fast is the surface area increasing when the length of an edge is   .

Accepted Answer

The answer of The volume of a cube is increasing...

Question 2

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

Use the graph of the function f to find the value(s) of x at which f is not differentiable.

Accepted Answer

A) ± 2 
B) 0 
C) 2 
D) -2 
A) ± 2 
B) 0 
C) 2 
D) -2

Question 4

Find   in terms of x and y.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Suppose the total cost in maunufacturing x units of a certain product is C (x) dollars.
a.What does   measure? Give units. 
b.What can you say about the sign of   ? 
c.Given that   , estimate the additional cost in producing the 3001st unit of the product.

Accepted Answer

The answer of Suppose the total cost in maunufacturing x...

Question 6

Find the point(s) on the graph of the function at which the tangent line has the indicated slope. g (x) =   x3   x2 - 29x - 3 mtan = -2

Accepted Answer

A)    
B) (3, -2) and (-9, -2) 
C) (-2, -37) 
D)    and   
A)    
B) (3, -2) and (-9, -2) 
C) (-2, -37) 
D)    and

Question 7

Let y = 1/x.
a.Find $\Delta$x and $\Delta$y if x changes from 1 to 1.03.Round to six decimal places, if necessary.
b.Find the differential dy, and use it to approximate $\Delta$y if x changes from 1 to 1.03.
c.Compute $\Delta$y - dy, the error in approximating $\Delta$y by dy.

Accepted Answer

a. 0.03, –

Question 8

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

Accepted Answer

The answer of Use implicit differentiation to find an equation...

Question 9

A water trough is 20 m long and a cross-section has the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 60 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of   , how fast is the water level rising when the water is   cm deep? Round the result to the nearest hundredth.

Accepted Answer

The answer of A water trough is 20 m long...

Question 10

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x (t) =  sin t, where t is in seconds and x in centimeters.
Find the velocity at time t.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Find the linearization L (x) of the function at
a.

Accepted Answer

A)    x -   
B)    x +   
C)    x -   
D)    x +   
A)    x -   
B)    x +   
C)    x -   
D)    x +

Question 12

Find   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Find the limit.

Accepted Answer

A) 1 
B) 2 
C)    cos 1 
D)    sin 1 
E) 0 
A) 1 
B) 2 
C)    cos 1 
D)    sin 1 
E) 0

Question 14

Find an equation of the tangent line to the curve   at the point (1, 1).

Accepted Answer

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

Question 15

Find an equation of the tangent line to the given curve at the indicated point.

Accepted Answer

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

Question 16

Suppose that f and g are functions that are differentiable at x = 1 and that f (1) = 1,   (1) = -2, g (1) = 3, and   (1) = 4. Find   .

Accepted Answer

The answer of Suppose that f and g are functions...

Question 17

If

Accepted Answer

The answer of If  ...

Question 18

Determine the constants A, B, and C such that the parabola   passes through the point   and is tangent to the line y =   x +   at the point where x = -3.

Accepted Answer

A= -2 , B=

Question 19

Find the tangent line to the parabola   at the point

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 20

The top of a ladder slides down a vertical wall at a rate of   m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

The volume of a cube is increasing at a rate of . How fast is the surface area increasing when the length of an edge is .

Find the derivative of the function.

Use the graph of the function f to find the value(s) of x at which f is not differentiable.

Find in terms of x and y.

Suppose the total cost in maunufacturing x units of a certain product is C (x) dollars. a.What does measure? Give units. b.What can you say about the sign of ? c.Given that , estimate the additional cost in producing the 3001st unit of the product.

Find the point(s) on the graph of the function at which the tangent line has the indicated slope. g (x) = x³ x² - 29x - 3 m_tan = -2

Let y = 1/x. a.Find $\Delta$ x and $\Delta$ y if x changes from 1 to 1.03.Round to six decimal places, if necessary. b.Find the differential dy, and use it to approximate $\Delta$ y if x changes from 1 to 1.03. c.Compute $\Delta$ y - dy, the error in approximating $\Delta$ y by dy.

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x (t) = sin t, where t is in seconds and x in centimeters. Find the velocity at time t.

Find the linearization L (x) of the function at a.

Find .

Find the limit.

Find an equation of the tangent line to the curve at the point (1, 1).

Find an equation of the tangent line to the given curve at the indicated point.

Suppose that f and g are functions that are differentiable at x = 1 and that f (1) = 1, (1) = -2, g (1) = 3, and (1) = 4. Find .

If

Determine the constants A, B, and C such that the parabola passes through the point and is tangent to the line y = x + at the point where x = -3.

Find the tangent line to the parabola at the point

The top of a ladder slides down a vertical wall at a rate of m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?

Functions and Limits

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 2: Derivatives

The volume of a cube is increasing at a rate of . How fast is the surface area increasing when the length of an edge is .

Find the derivative of the function.

Use the graph of the function f to find the value(s) of x at which f is not differentiable.

Find in terms of x and y.

Suppose the total cost in maunufacturing x units of a certain product is C (x) dollars. a.What does measure? Give units. b.What can you say about the sign of ? c.Given that , estimate the additional cost in producing the 3001st unit of the product.

Find the point(s) on the graph of the function at which the tangent line has the indicated slope. g (x) = x3 x2 - 29x - 3 mtan = -2

Let y = 1/x. a.Find Δ\DeltaΔ x and Δ\DeltaΔ y if x changes from 1 to 1.03.Round to six decimal places, if necessary. b.Find the differential dy, and use it to approximate Δ\DeltaΔ y if x changes from 1 to 1.03. c.Compute Δ\DeltaΔ y - dy, the error in approximating Δ\DeltaΔ y by dy.

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x (t) = sin t, where t is in seconds and x in centimeters. Find the velocity at time t.

Find the linearization L (x) of the function at a.

Find .

Find the limit.

Find an equation of the tangent line to the curve at the point (1, 1).

Find an equation of the tangent line to the given curve at the indicated point.

Suppose that f and g are functions that are differentiable at x = 1 and that f (1) = 1, (1) = -2, g (1) = 3, and (1) = 4. Find .

If

Determine the constants A, B, and C such that the parabola passes through the point and is tangent to the line y = x + at the point where x = -3.

Find the tangent line to the parabola at the point

The top of a ladder slides down a vertical wall at a rate of m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?

Functions and Limits

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Find the point(s) on the graph of the function at which the tangent line has the indicated slope. g (x) = x³ x² - 29x - 3 m_tan = -2

Let y = 1/x. a.Find $\Delta$ x and $\Delta$ y if x changes from 1 to 1.03.Round to six decimal places, if necessary. b.Find the differential dy, and use it to approximate $\Delta$ y if x changes from 1 to 1.03. c.Compute $\Delta$ y - dy, the error in approximating $\Delta$ y by dy.