Question 1

Find the derivative of the function.
f (x) = x sin8 x

Accepted Answer

Question 2

The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 8 seconds.

Accepted Answer

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

Question 3

A point moves along the curve   . When the point is at   , its x-coordinate is increasing at the rate of 3 units per second. How fast is its y-coordinate changing at that instant of time?

Accepted Answer

A)    units/sec 
B)    units/sec 
C)    units/sec 
D)    units/sec 
A)    units/sec 
B)    units/sec 
C)    units/sec 
D)    units/sec

Question 4

A turkey is removed from the oven when its temperature reaches 175 S1U1P1$\circ$S1S1P0 F and is placed on a table in a room where the temperature is 70   F. After 10 minutes the temperature of the turkey is 161 S1U1P1$\circ$S1S1P0 F and after 20 minutes it is 149 S1U1P1$\circ$S1S1P0 F. Use a linear approximation to predict the temperature of the turkey after 30 minutes.

Accepted Answer

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

Question 5

Find the first and the second derivatives of the function.

Accepted Answer

The answer of Find the first and the second derivatives...

Question 6

Find the derivative of the following function and calculate it for x =   to the nearest tenth.

Accepted Answer

A) 0.2 
B)    
C) 1.1 
D) 0.3 
E) 0.1 
A) 0.2 
B)    
C) 1.1 
D) 0.3 
E) 0.1

Question 7

If

Accepted Answer

The answer of If  ...

Question 8

Differentiate.

Accepted Answer

The answer of Differentiate.  ...

Question 9

Gravel is being dumped from a conveyor belt at a rate of   ft /min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is   ft high? Round the result to the nearest hundredth.

Accepted Answer

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

Question 10

The circumference of a sphere was measured to be   cm with a possible error of   cm. Use differentials to estimate the maximum error in the calculated volume.

Accepted Answer

The answer of The circumference of a sphere was measured...

Question 11

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 12

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of   ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.

Accepted Answer

The answer of A baseball diamond is a square with...

Question 13

Plot the graph of the function f in an appropriate viewing window.
f (x) = 2x   - 5x   + 4x   + 37

Accepted Answer

The answer of Plot the graph of the function f...

Question 14

Find the first and the second derivatives of the function.

Accepted Answer

The answer of Find the first and the second derivatives...

Question 15

Find the equation of the tangent to the curve at the given point.

Accepted Answer

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

Question 16

Find the derivative of the function.

Accepted Answer

A)    t5   t4 
B)    t4   t3 
C)    t4   t3   
D)    t5   t4   
A)    t5   t4 
B)    t4   t3 
C)    t4   t3   
D)    t5   t4

Question 17

Let   . 
a.Sketch the graph of f.
b.For what values of x is f differentiable?
c.Find a formula for   .

Accepted Answer

The answer of Let   . 
a.Sketch the graph...

Question 18

The volume of a right circular cone of radius r and height h is   . Suppose that the radius and height of the cone are changing with respect to time t. 
a.Find a relationship between   ,   , and   . 
b.At a certain instant of time, the radius and height of the cone are 12 in.and 13 in.and are increasing at the rate of 0.2 in./sec and 0.5 in./sec, respectively.How fast is the volume of the cone increasing?

Accepted Answer

The answer of The volume of a right circular cone...

Question 19

Find the differential of the function at the indicated number.

Accepted Answer

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

Question 20

Differentiate.

Accepted Answer

The answer of Differentiate.  ...

Find the derivative of the function. f (x) = x sin⁸ x

The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 8 seconds.

A point moves along the curve . When the point is at , its x-coordinate is increasing at the rate of 3 units per second. How fast is its y-coordinate changing at that instant of time?

Find the first and the second derivatives of the function.

Find the derivative of the following function and calculate it for x = to the nearest tenth.

If

Differentiate.

Gravel is being dumped from a conveyor belt at a rate of ft /min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is ft high? Round the result to the nearest hundredth.

The circumference of a sphere was measured to be cm with a possible error of cm. Use differentials to estimate the maximum error in the calculated volume.

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.

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.

Plot the graph of the function f in an appropriate viewing window. f (x) = 2x - 5x + 4x + 37

Find the first and the second derivatives of the function.

Find the equation of the tangent to the curve at the given point.

Find the derivative of the function.

Let . a.Sketch the graph of f. b.For what values of x is f differentiable? c.Find a formula for .

Find the differential of the function at the indicated number.

Differentiate.

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

Find the derivative of the function. f (x) = x sin8 x

The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 8 seconds.

A point moves along the curve . When the point is at , its x-coordinate is increasing at the rate of 3 units per second. How fast is its y-coordinate changing at that instant of time?

Find the first and the second derivatives of the function.

Find the derivative of the following function and calculate it for x = to the nearest tenth.

If

Differentiate.

Gravel is being dumped from a conveyor belt at a rate of ft /min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is ft high? Round the result to the nearest hundredth.

The circumference of a sphere was measured to be cm with a possible error of cm. Use differentials to estimate the maximum error in the calculated volume.

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.

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? Round the result to the nearest hundredth.

Plot the graph of the function f in an appropriate viewing window. f (x) = 2x - 5x + 4x + 37

Find the first and the second derivatives of the function.

Find the equation of the tangent to the curve at the given point.

Find the derivative of the function.

Let . a.Sketch the graph of f. b.For what values of x is f differentiable? c.Find a formula for .

Find the differential of the function at the indicated number.

Differentiate.

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 derivative of the function. f (x) = x sin⁸ x

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.