Question 1

Compute the area of the finite region bounded by the graphs of the functions $y = 5 x ^ { 2 }$ ,and $y = - 5 x ^ { 2 } - 20 x + 80$ .

Accepted Answer

A) 360 
B) 320 
C) 280 
D) 240 
A) 360 
B) 320 
C) 280 
D) 240

Question 2

Solve the given initial value problem for y = f (x). $\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }$ where y = 6 when x = 1

Accepted Answer

A)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14 + 6$ 
B)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14$ 
C)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| + 6$ 
D)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right|$ 
A)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14 + 6$ 
B)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| - \frac { 1 } { 2 } \ln 14$ 
C)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right| + 6$ 
D)  $y = \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 10 x + 3 \right|$

Question 3

Suppose the marginal cost is $C ^ { \prime } ( x ) = e ^ { - 0.4 x }$ ,where x is measured in units of 300 items and the cost is measured in units of $10,000.Find the cost corresponding to the production interval [300,1,500].Round to the nearest dollar.

Accepted Answer

A) $13,375 
B) $5,350 
C) $9,029 
D) $2,140 
A) $13,375 
B) $5,350 
C) $9,029 
D) $2,140

Question 4

The chief economist for a meat-packing plant estimates that if L worker-hours of labor are employed each week,the number of pounds of meat made ready for sale will be given by $Q ( L ) = 650 L ^ { 3 / 4 }$ .Find the average weekly output as labor varies from 480 to 790 hours.Round to the nearest pound.

Accepted Answer

A) 82,069 pounds 
B) 73,954 pounds 
C) 34,248 pounds 
D) 86,461 pounds 
A) 82,069 pounds 
B) 73,954 pounds 
C) 34,248 pounds 
D) 86,461 pounds

Question 5

Find the average value of the function $f ( x ) = \frac { x } { 4 x + 1 }$ over the interval [1,3].Round your answer to two decimal places.

Accepted Answer

A) 0.28 
B) 1.22 
C) 0.44 
D) 0.22 
A) 0.28 
B) 1.22 
C) 0.44 
D) 0.22

Compute the area of the finite region bounded by the graphs of the functions $y = 5 x ^ { 2 }$ ,and $y = - 5 x ^ { 2 } - 20 x + 80$ .

Solve the given initial value problem for y = f (x). $\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }$ where y = 6 when x = 1

Suppose the marginal cost is $C ^ { \prime } ( x ) = e ^ { - 0.4 x }$ ,where x is measured in units of 300 items and the cost is measured in units of $10,000.Find the cost corresponding to the production interval [300,1,500].Round to the nearest dollar.

Find the average value of the function $f ( x ) = \frac { x } { 4 x + 1 }$ over the interval [1,3].Round your answer to two decimal places.

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

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Exam 5: Itegration

Compute the area of the finite region bounded by the graphs of the functions y=5x2y = 5 x ^ { 2 }y=5x2 ,and y=−5x2−20x+80y = - 5 x ^ { 2 } - 20 x + 80y=−5x2−20x+80 .

Solve the given initial value problem for y = f (x). dydx=x+5x2+10x+3\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }dxdy​=x2+10x+3x+5​ where y = 6 when x = 1

Suppose the marginal cost is C′(x)=e−0.4xC ^ { \prime } ( x ) = e ^ { - 0.4 x }C′(x)=e−0.4x ,where x is measured in units of 300 items and the cost is measured in units of $10,000.Find the cost corresponding to the production interval [300,1,500].Round to the nearest dollar.

Find the average value of the function f(x)=x4x+1f ( x ) = \frac { x } { 4 x + 1 }f(x)=4x+1x​ over the interval [1,3].Round your answer to two decimal places.

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Compute the area of the finite region bounded by the graphs of the functions $y = 5 x ^ { 2 }$ ,and $y = - 5 x ^ { 2 } - 20 x + 80$ .

Solve the given initial value problem for y = f (x). $\frac { d y } { d x } = \frac { x + 5 } { x ^ { 2 } + 10 x + 3 }$ where y = 6 when x = 1

Suppose the marginal cost is $C ^ { \prime } ( x ) = e ^ { - 0.4 x }$ ,where x is measured in units of 300 items and the cost is measured in units of $10,000.Find the cost corresponding to the production interval [300,1,500].Round to the nearest dollar.

Find the average value of the function $f ( x ) = \frac { x } { 4 x + 1 }$ over the interval [1,3].Round your answer to two decimal places.