Final Exam Spring 2020 PDF

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APplied Calculus Final Exam...

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R.I.T Dubai COS-MATH-161 APPLIED CALCULUS SPRING 2020 FINAL EXAM - SEGMENT A Date: Wednesday April 29th, 2020 Duration: 30 minutes

Timing: 1:40 – 2:10 PM

For full credit, show purposeful details of your work for every single question clearly and neatly. Question 1: Discuss the validity of each statement. If the statement is always true, support with it an example. If not, provide a counterexample. (1 mark each) a. The derivative of a product is the product of the derivatives.

b. The derivative of a constant times a function is zero.

__________________________________________________________________________________________________ Question 2: Air is being pumped into a spherical balloon at a rate of 5 cm 3 /min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm. Include appropriate unit for your answer. (2.5 marks) Volume of Sphere:

4 V = π (r (t ))3 3

__________________________________________________________________________________________________ Question 3: A set of data is modelled by s(t) = 70 ln t + 5 where s(t) is the number of TV subscribers (in millions) in year (t = 0 corresponds to 1980). Use this model to estimate rate of change in number of subscribers in 2015. Include appropriate unit for your answer. (2 marks)

__________________________________________________________________________________________________ Question 4: Evaluate the following definite integrals by referring to the given figure. (0.5 mark each)

c

a.

∫ f ( x ) dx=¿ 0

a

b.

∫ f ( x ) dx=¿ b

b

c.

∫ f ( x ) dx=¿ b

__________________________________________________________________________________________________ Question 5: Use the given graph to set up the integral for the area of the shaded region. Do not solve the integral. Only set up the integral. (2 marks)

R.I.T Dubai COS-MATH-161 APPLIED CALCULUS SPRING 2020 FINAL EXAM - SEGMENT B Date: Wednesday April 29th, 2020 Duration: 30 minutes

Timing: 2:20 – 2:50 PM

For full credit, show purposeful details of your work for every single question clearly and neatly. Question 6: Find the total income produced by a continuous income stream in the first 4 years if the rate of flow is f(t) = 2,500.

Simplify your answer. (2 marks) b

Total Income =

∫ f (t ) dt a

Question 7: Find the consumers’ surplus at a price level of P = D(x) = 200 – 0.2x. Simplify your answer. (4 marks)

[ D ( x )−¿ p] dx CS =

x

∫¿ 0

p=¿

$120 for the price-demand equation

Question 8: Find the producer’s surplus at a price level of x

2

. Simplify your answer. (4 marks)

[¿ p−S (x)] dx PS =

x

∫¿ 0

p=¿ $4 for the price-supply equation P = S(x) = 2 + 0.02

R.I.T Dubai COS-MATH-161 APPLIED CALCULUS SPRING 2020 FINAL EXAM - SEGMENT C Date: Wednesday April 29th, 2020 Duration: 30 minutes

Timing: 3:00 – 3:30 PM

For full credit, show purposeful details of your work for every single question clearly and neatly. Question 9: Suppose that in a memory experiment, the rate of memorizing is given by

2 m ' ( t )=−0.003 t + 0.2t

where m ' ( t ) is the memory rate , in words per minute. How many words in total are memorized in the first 10 minutes? (3 marks)

Question 10: An annuity is a fund into which one makes equal payments at regular intervals. The fund earns interest at rate 10% compounded continuously per year, and the fixed deposit of AED4,000 are made each year. At the beginning, there is no fund in the annuity account. a. Write a differential equation that expresses the funding amount per year. (2 marks) b. Solve for the particular solution of the differential equation you obtained in part ‘ a’. (4 marks) c. Find the annuity balance after 10 years. (1 mark)...