MTH 252 Final Exam No Calc Portion Winter Term x

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1 MTH 5 Final Exam No Calc Portion Winter Term 7 Name 1. Evaluate each integral. All solutions must be fully substantiated by the work presented on this paper. (5 points each) a. 3x dx 8 3x x b. xe dx Page 1 of 9

2 MTH 5 Final Exam - 71 c. x e dx 16 + e x d. 3 9 θ dθ + θ Page of 9

3 MTH 5 Final Exam Evaluate each limit. Show all relevant work. (5 points each) a. x lim x ln x ( 5e + 7) ( ) b. lim x ln( x) x + Page 3 of 9

4 MTH 5 Final Exam Find the absolute maximum value of the function f ( x) = x 3 + 3x 9 x + over the interval [,]. All relevant work must be shown on this page in a well-organized and well-documented manner. (8 points). A certain function, y = g( x) g ( ) = and that g ( x) = x + x. Which does g( x), is continuous and differentiable at all points. You are told that maximum point or a local minimum point? Explain your reasoning! ( points) y = have at x = : a local Page of 9

5 MTH 5 Final Exam - 71 dt 5. Evaluate using appropriate analysis and showing all relevant work. (8 points) 8 3 t 7 ( ) Page 5 of 9

6 MTH 5 Final Exam Fill in each blank based upon Figure 6. No work need be, nor should be, shown. (1.5 points each) y y a. A = b. B = c. f ( x ) dx = d. f ( x ) dx = A x B Figure 1 y = f ( x) Figure 6 y = f x ( ) x e. f ( x ) dx = f. ( ) f x dx = g. ( ) f x dx = h. If F is an antiderivative of f and F ( ) = 8, then ( ) F =. i. If F is an antiderivative of f and F ( ) = 1, then the absolute minimum value of F over the interval [, ] is. j. If F is an antiderivative of f and F ( ) = 1, then the absolute maximum value of F over the interval [, ] is. Page 6 of 9

7 MTH 5 Final Exam - 71 MTH 5 Final Exam Calc Portion Winter Term 7 Name Please use your calculator for all calculations on this portion of the test. 1. Consider f 3 ( x) = x x. (1 points total) a. Find on your calculator the completely simplified form of f ( x). State the result. b. State the critical numbers of f. No explanation necessary. c. Build an increasing/decreasing table for f and then state the local minimum and maximum points on f. Page 7 of 9

8 MTH 5 Final Exam The equations of the skew lines in figure 1 and are 1 y = x + and y = x. a. Use an integral (integrals) whose variable is x to find the area of the triangular region in Figure 1. Make sure that you annotate Figure 1 in a manner consistent with that discussed and illustrated in class. (5 points) Figure 1 b. Use an integral (integrals) whose variable is y to find the area of the triangular region in Figure. Make sure that you annotate Figure 1 in a manner consistent with that discussed and illustrated in class. (7 points) Figure Page 8 of 9

9 MTH 5 Final Exam Suppose that T() t was the temperature ( O F) at the center of an uneaten hunk of cheese t hours after it was taken out of the refrigerator and that T ( t) 36(.3 t ) =. Suppose that.5 hours after the cheese was taken out of the refrigerator, the temperature at the center of the hunk of cheese was 68.5 O F. What, to the nearest tenth of a degree, was the temperature at the center of the hunk of cheese 3 hours later? (7 points). Suppose that Dt () = 1 +.sin.17( t 8) Madrid on the t th after January 1. Find the average value of Dt ( ) over [ ] 1 th and state the practical meaning of the average value 1. (5 points) is the average number of daylight hours in,3 to the nearest 1 Note: While the applied function is not really continuous, the formula used to generate the output is continuous and we commonly accept the average value of the continuous function as the average value of the applied function. Page 9 of 9

You may hold onto this portion of the test and work on it some more after you have completed the no calculator portion of the test.

MTH 5 Winter Term 010 Test 1- Calculator Portion Name You may hold onto this portion of the test and work on it some more after you have completed the no calculator portion of the test. 1. Consider the