Question 1

The Laplace transform  of a function  is given by the formula.  Find  if

Accepted Answer

A)   
B)   
C)   
D)   
E)    A

Question 2

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)    B

Question 3

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)    C

Question 4

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

You are saving for your retirement by investing $700 per month in an annuity with a guaranteed interest rate of 6% per year. You increase the amount you invest at the rate of 4% per year. With continuous investment and compounding, how much will you have accumulated in the annuity by the time you retire in 25 years?

Accepted Answer

A)  $7,406.31
B)  $4,209,782.72
C)  $740,631.04
D)  $38,218.71
E)  $165,257.12

Question 7

Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate.  Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $__________ PV = $__________

Accepted Answer

The answer of Find the total value of the given...

Question 8

For the differential equation, find the particular solution if  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Find the general solution of the differential equation.  Solve for  as a function of  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

For the given differential equation, find the particular solution  when  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Match between columns Premises:

Accepted Answer

The Answer of <img src="https://d2lvgg3v3hfg70.cloudfront.net/TBX8650/11ebfe6a_2cea_6829_96cc_bb72724c409b_TBX8650_11.jpg" alt=" " class="answers-bank-image d-inline" rel="preload" is...

Question 12

Suppose your annual income is  dollars per year, where t represents the number of years since you began your job, while your annual expenses are  dollars per year. Find the area between the graphs of  and  for  .

Accepted Answer

A)  Area = $197,100
B)  Area = $67,200
C)  Area = $129,900
D)  Area = $65,400
E)  Area = $62,700

Question 13

The Megabucks Corporation is issuing a 5-year bond paying 8% interest. An investor wishes to buy the rights to receive the interest on $90,000 worth of these bonds and seeks a 6% rate of return. If the investor payments are made continuously, what will the investor pay?

Accepted Answer

A)  $281,983.06
B)  $31,101.81
C)  $311.02
D)  $120,000.00
E)  $1,866.11

Question 14

Sales of the text "Calculus and You" have been declining continuously at an annual rate of 6%. Assuming that "Calculus and You" currently sell 6,000 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text. Use the formula for continuously compounded interest with a negative rate.

Accepted Answer

A)  2,500,000 copies
B)  600,000 copies
C)  100,000 copies
D)  1,000,000 copies
E)  5,000,000 copies

Question 15

Find the average of the function  over 0, 8 .

Accepted Answer

A)  Average = 
B)  Average = 
C)  Average = 
D)  Average = 
E)  Average =

Question 16

Find the average of the function  over 0, 8 .

Accepted Answer

A)  Average = 180
B)  Average = 157
C)  Average = 160
D)  Average = 1440
E)  Average = 179

Question 17

The annual revenue earned by Wal-Mart in the fiscal years ending January 31, 1994 to January 31, 2003 can be approximated by  billion dollars per year  where  is time in years  represents January 31, 2000). Suppose that, from January 1999 on, Wal-Mart invested its revenue in an investment that depreciated continuously at a rate of 4% per year. What, to the nearest $10 billion, would the total value of Wal-Mart s revenues have been by the end of January 2003?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Decide whether the integral converges. If the integral converges, compute its value.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

If you invest $8,000 at 12% interest compounded continuously, what is the average amount in your account over one year? Round your answer to the nearest cent.

Accepted Answer

A)  $8,499.79
B)  $8,598.43
C)  $8,697.07
D)  $8,302.51
E)  $8,401.15

Question 20

Find the general solution of the differential equation.  Solve for  as a function of  . NOTE: Use the symbol C to enter the constant.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 7: Further Integration Techniques and Applications of the Integral

The Laplace transform of a function is given by the formula. Find if

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Find the total value of the given income stream and also find its present value (at the beginning of the given interval)using the given interest rate. Please enter your answer in the form TV = , PV = . Give the answer to the nearest cent if necessary. TV = $ PV = $

For the differential equation, find the particular solution if .

Find the general solution of the differential equation. Solve for as a function of .

For the given differential equation, find the particular solution when .

Find the areas of the indicated regions. Choose the correct letter for each question.

Suppose your annual income is dollars per year, where t represents the number of years since you began your job, while your annual expenses are dollars per year. Find the area between the graphs of and for .

The Megabucks Corporation is issuing a 5-year bond paying 8% interest. An investor wishes to buy the rights to receive the interest on $90,000 worth of these bonds and seeks a 6% rate of return. If the investor payments are made continuously, what will the investor pay?

Find the average of the function over 0, 8 .

Find the average of the function over 0, 8 .

Decide whether the integral converges. If the integral converges, compute its value.

If you invest $8,000 at 12% interest compounded continuously, what is the average amount in your account over one year? Round your answer to the nearest cent.

Find the general solution of the differential equation. Solve for as a function of . NOTE: Use the symbol C to enter the constant.