Practice DEPARTMENTAL FINAL EXAMINATION 2014 MATH M 119 BRIEF SURVEY OF CALCULUS

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1 Practice DEPARTMENTAL FINAL EXAMINATION 2014 MATH M 119 BRIEF SURVEY OF CALCULUS Directions DO NOT OPEN this test booklet until you are asked to do so. There are seven pages on this eam with 20 problems You MUST get a new eam from the proctor if your eam is incomplete. PRINT your name and student ID# and check your section below. You have two hours to complete this eamination. No scratch paper if you need etra paper use the back of a test booklet page. Sharing calculators is not permitted. The only permissible calculator is the TI 30XA NO notes, books; Cell phones should be OFF. Earpieces are not permitted. NEATNESS COUNTS. CORRECT NOTATION COUNTS. To receive credit show supporting work. NAME (Print Clearly) UNIV ID# Do Not Write In This Area Page 2 4 Page 3 10 Page 4 7 Page 5 8 Page 6 8 Page 7 6 Page 8 7 TOTAL 50 Math M119 Practice Final Eam page 1 of 8

2 1. Sketch a graph of the first derivative for the function depicted below. Make certain that your sketch shows intercepts eactly where you want them to be. Also make sure your graph of is above (below) the ais just when it s supposed to be. (2) 2. Suppose that is a function with and Use a local linear approimation to estimate (2) Math M119 Practice Final Eam page 2 of 8

3 3. Given 2 Find 4. Given ln 3 Find 1 5. Find the derivative of the function 6. Given 8 Find and simplify. 7. Find the quantity q which maimizes profit if the total revenue and total cost (in dollars) are given by , Math M119 Practice Final Eam page 3 of 8

4 8. Write an equation of the tangent line to the curve 1 at A state park charges $100 for an annual pass. At this rate 750 people purchase passes every year. For each $5 decrease in price 15 more people purchase a pass. What price should the park charge in order to maimize revenue? Use calculus and show your work. (2) Estimate the value of the definite integral d 10 2 by using n = 4 (Δ = 2) and by computing: a. The left hand sum (1) b. The right hand sum (1) c. The average (1) Math M119 Practice Final Eam page 4 of 8

5 11. Find each indefinite integral: 4 a. ( 7 ) d b. (3t 6 4 8e t ) dt 12. Find an antiderivative F() with 9 and F(0) = 1. F ( ) e F() = (2) (4 3 5) d 1 Math M119 Practice Final Eam page 5 of 8

6 e t dt d Find the present value of an income stream of $7000 per year for a 6 year period if the interest rate is 3% compounded continuously (give your answer to the nearest dollar). 17. Find the eact area under the graph of between = 0 and = 81. Show your work and simplify your answer. Math M119 Practice Final Eam page 6 of 8

7 18. Sketch a graph of the parabola: 4 12 and shade the region bounded by the function and the ais. Then carefully write the definite integral that would give the area of the shaded region. You do not have to evaluate the integral or find the area; just write the integral that would give the area. Carefully write the integral here: You do not have to evaluate the integral or find the area. (4) 19. The marginal cost of drilling an oil well depends on the depth at which you are drilling: drilling becomes more epensive, per meter, as you dig deeper into the earth. The fied costs are $100,000 and if is the depth in meters, the marginal costs are dollars per meter. What is the total cost of drilling a 200 meter well? Math M119 Practice Final Eam page 7 of 8

8 20. Consider the polynomial 6 restricted to the interval [ 1, 7] (a) Find any critical points (both 1 st and 2 nd coordinates) and classify each as a local ma, local min, or neither. (b) Find the global ma and the global min. (c) Find any inflection points (both 1 st and 2 nd coordinates). (d) Sketch a graph of the function. (7) Math M119 Practice Final Eam page 8 of 8