PLEASE MARK YOUR ANSWERS WITH AN X, not a circle! 2. (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) (a) (b) (c) (d) (e)...

Transcription

1 . Math 00, Exam November 0, 0. The Honor Code is in e ect for this examination. All work is to be your own. No calculators. The exam lasts for hour and min. Be sure that your name is on every page in case pages become detached. Be sure that you have all 0 pages of the test. PLEASE MARK YOUR ANSWERS WITH AN X, not a circle!. (a) (b) (c) (d) (e). (a) (b) (c) (d) (e).... (a) (b) (c) (d) (e). (a) (b) (c) (d) (e).... (a) (b) (c) (d) (e) 6. (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) 8. (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) 0. (a) (b) (c) (d) (e) Please do NOT write in this box. Multiple Choice.... Total

2 Multiple Choice.(6 pts.) Find the equation of the slant asymptote to the function f(x) = x +x +x + x + (a) y = x + (b) y =x + (c) y = x + (d) y =x + (e) y = x +.(6 pts.) Calculate the indefinite integral Z x + p x x dx (a) + p x + C (b) + x9/ 9 + C (c) x + x9/ 9 (e) x + p x + C + C (d) x (9/) + C

3 .(6 pts.) Estimate the area under the graph of y = f(x) betweenx = 0 and x = 6 using the Riemann sum which gives the right end point approximation with 6 approximating rectangles whose bases are of equal length (i.e. use R 6 ). 6 y y=f(x) 6 x - (a) R 6 = 0 (b) R 6 = (c) R 6 =0 (d) R 6 =8 (e) R 6 =.(6 pts.) In finding the approximate solution to x using Newton s method with initial approximation x =, what is x? (a) (b) 7 (c) (d) (e)

4 .(6 pts.) A ball is thrown upwards from a height of 0 feet above the surface of the planet Minerva with an initial velocity of 6 feet per second (at time t = 0). The ball has a constant acceleration of ft/sec. What is the maximum height (from the surface of the planet) reached by the ball? (a) ft (b) ft. (c) 9 ft. (d) 6 ft. (e) ft. 6.(6 pts.) The graph of the piecewise defined function g(x) is shown below. The graph consists of part of a circle and straight lines. Use the graph to calculate 0 y Z 8 g(x) dx x y = g(x) (a) + 8 (b) 6 (c) 6 8 (d) + (e) 9

5 7.(6 pts.) Let Find h 0 (x). h(x) = Z x + sin (t) dt. (a) x + sin (x ) (b) sin(x)cos(x) + sin (x ) (c) + sin (x) (d) sin(x)cos(x) ( + sin (x)) (e) + sin (x ) 8.(6 pts.) Calculate the indefinite integral Z p x + sin( x) p ; dx. x (a) (b) (c) (d) (e) x / x / x / x / x / + cos(p x) p x cos( p x) p x + C + C cos( p x)+c +cos(x)+c cos(x)+c

6 9.(6 pts.) An underground beer pipeline in the city of Bruges has sprung a leak which is gradually worsening. Your statistics suggest that beer is leaking from the pipeline at arateoft t + gallons per day, where t denotes the number of days after the leak started. How many gallons of beer will have leaked in the first days after the leak started? (a) gallons (b) 6 gallons (c) 8 gallons (d) 7 gallons (e) 9 gallons 0.(6 pts.) Evaluate the following definite integral Z 0 sin x cos x dx (a) (b) (c) (d) (e) 6

7 Partial Credit You must show your work on the partial credit problems to receive credit!.( pts.) (a) Evaluate the definite integral Z and the limit definition of the definite integral. n(n +). Hint: n = 0 x dx using the right endpoint approximation (b) Verify your answer using the fundamental theorem of calculus. 7

8 .( pts.) A manufacturer needs to make a cylindrical can (top included ) that will hold 000 cm of liquid. Find the dimensions of the can (values of r and h) that will minimize the amount of material used to make the can. (Exact values such as p, p,, p, etc... should not be converted to a decimal approximation.) Note that the surface area of a cylinder with no top or bottom is rh cm. r = cm h = cm. 8

9 .( pts.) Find the area of the bounded region between the curves y = x x + and y =7 x +x. 9

10 .( pts.) You will earn points if your instructor can read your name easily on the front page of the exam and you mark the answer boxes with an X (as opposed to a circle or any other mark). Rough Work 0