Question 1

Evaluate the following integral: $\int 3 e ^ { 7 x } d x$

Accepted Answer

A)  $\frac { 3 } { 7 } e ^ { 7 x } + C$ 
B)  $3 e ^ { 7 x } + C$ 
C)  $21 e ^ { 7 x } + C$ 
D)  $\frac { 3 } { 8 } e ^ { 8 x } + C$ 
A)  $\frac { 3 } { 7 } e ^ { 7 x } + C$ 
B)  $3 e ^ { 7 x } + C$ 
C)  $21 e ^ { 7 x } + C$ 
D)  $\frac { 3 } { 8 } e ^ { 8 x } + C$

Question 2

Sketch the region R and then use calculus to find the area of R.R is the region between the curve $y = x ^ { 3 }$ and the line y = 18x for x  $\geq$ 0.

Accepted Answer

A) 20.25 
B) 4.5 
C) 0 
D) 81 
A) 20.25 
B) 4.5 
C) 0 
D) 81

Question 3

The output at a certain plant is $Q = 0.06 x ^ { 2 } + 0.15 x y + 0.05 y ^ { 2 }$ units per day,where x is the number of hours of skilled labor used and y is the number of hours of unskilled labor used.Currently 60 hours of skilled labor and 150 hours of unskilled labor are used each day.Use calculus to estimate the change in unskilled labor that should be made to offset a 1 hour increase in skilled labor so that output will remain the same.Round your answer to two decimal places,if necessary.

Accepted Answer

A) No change 
B) An increase of 1.24 hours 
C) A decrease of 1.24 hours 
D) It cannot be determined 
A) No change 
B) An increase of 1.24 hours 
C) A decrease of 1.24 hours 
D) It cannot be determined

Question 4

What is the rate of change of $f ( t ) = \frac { 2 t - 7 } { t + 6 }$ with respect to t when t = 13?

Accepted Answer

A) -19 
B) 19 
C)  $\frac { 1 } { 19 }$ 
D)  $- \frac { 1 } { 19 }$ 
A) -19 
B) 19 
C)  $\frac { 1 } { 19 }$ 
D)  $- \frac { 1 } { 19 }$

Question 5

The fraction of television sets manufactured by a certain company that are still in working condition after t years of use is approximately $f ( t ) = e ^ { - 0.2 t }$ .What fraction can be expected to fail before 2 years of use? Round your answer to two decimal places,if necessary.

Accepted Answer

A) 1.49 
B) 0.91 
C) 0.67 
D) 0.33 
A) 1.49 
B) 0.91 
C) 0.67 
D) 0.33

Evaluate the following integral: $\int 3 e ^ { 7 x } d x$

Sketch the region R and then use calculus to find the area of R.R is the region between the curve $y = x ^ { 3 }$ and the line y = 18x for x $\geq$ 0.

What is the rate of change of $f ( t ) = \frac { 2 t - 7 } { t + 6 }$ with respect to t when t = 13?

The fraction of television sets manufactured by a certain company that are still in working condition after t years of use is approximately $f ( t ) = e ^ { - 0.2 t }$ .What fraction can be expected to fail before 2 years of use? Round your answer to two decimal places,if necessary.

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Exam 12: Calculus Practice Questions

Evaluate the following integral: ∫3e7xdx\int 3 e ^ { 7 x } d x∫3e7xdx

Sketch the region R and then use calculus to find the area of R.R is the region between the curve y=x3y = x ^ { 3 }y=x3 and the line y = 18x for x ≥\geq≥ 0.

What is the rate of change of f(t)=2t−7t+6f ( t ) = \frac { 2 t - 7 } { t + 6 }f(t)=t+62t−7​ with respect to t when t = 13?

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Evaluate the following integral: $\int 3 e ^ { 7 x } d x$

Sketch the region R and then use calculus to find the area of R.R is the region between the curve $y = x ^ { 3 }$ and the line y = 18x for x $\geq$ 0.

What is the rate of change of $f ( t ) = \frac { 2 t - 7 } { t + 6 }$ with respect to t when t = 13?