HAND IN PART. Prof. Girardi Math 142 Spring Exam 1. NAME: key

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1 HAND IN PART Prof. Girardi Math 4 Spring 4..4 Exam MARK BOX problem points 7 % NAME: key PIN: INSTRUCTIONS The mark box above indicates the problems along with their points. Check that your copy of the exam has all of the problems. You may not use an electronic device, a calculator, books, personal notes. On Problem, fill in the blanks. As you were warned, if you do not make at least half of the points on Problem, then your score for the entire exam will be whatever you made on Problem. 4 Problems are multiple choice. First, indicate to yourself your answers directly on the STATEMENT OF MULTIPLE CHOICE PROBLEMS part. Once finished with the multiple choice problems, go back to the HAND IN PART and indicate your answers on the table provided. Hand in the HAND IN PART. You can take the STATEMENT OF MULTIPLE CHOICE PROBLEMS part home with you so you can check your answers once the solutions are posted. 5 During this exam, do not leave your seat unless you have permission. If you have a question, raise your hand. When you finish: put your pencil down and raise your hand. 6 This exam covers from Calculus by Stewart, 6 th ed., ET: , 7.8,..

2 . Fill in the blanks each worth point. a. If u, then du u = ln u b. If a is a constant and a > but a, then a u du = au c. cos u du = sin u d. sec u du = tan u e. sec u tan u du = sec u f. sin u du = - cos u g. csc u du = - cot u h. csc u cot u du = - csc u or i. tan u du = ln sec u = - ln cos u or j. cot u du = - ln csc u = ln sin u or k. sec u du = ln sec u + tan u = - ln sec u tan u or l. csc u du = - ln csc u + cot u = ln csc u cot u m. If a is a contant and a > then du = a u n. If a is a contant and a > then du = a +u a tan- u ln a sin- u a o. If a is a contant and a > then u du = u u a a sec- a p. Partial Fraction Decomposition. If one wants to integrate fx gx a + C and [degree of f] [degree of g], then one must first do long division q. Integration by parts formula: u dv = uv vdu where f and g are polyonomials r. Trig. Substitution: recall that the integrand is the function you are integrating if the integrand involves a u, then one makes the substitution u = s. Trig. Substitution: if the integrand involves a + u, then one makes the substitution u = t. Trig. Substitution: if the integrand involves u a, then one makes the substitution u = a sin θ a tan θ a sec θ u. Trig. Formula... your answer should involve trig functions of θ, and not of θ: sinθ = sin θ cos θ. v&w. Trig. Formula... cosθ should appear in your answer & notice the already stuck out front: cos θ = + cos θ and sin θ = cos θ. x. trig formula... since cos θ + sin θ =, we know that the corresponding relationship beween tangent i.e., tan and secant i.e., sec is + tan θ = sec θ. y. arcsin - = -π 6 RADIANS. your answer should be an angle z. By definition, the sequence {a n } n= of real numbers converges to the real number L provided for each ɛ > there exists a natural number N so that if the natural number n satisfies n > or N, then L a n < ɛ. 5n ä n + n 7n 8 + 9n + 5 = -5n b n + n 7n 7 + 9n = DNE or n c. 7 6n n 4n 7 + 9n + 5 = 6 4 or 9 d. 6n 7 6n n 4n 7 + 9n + 5 = 6 4 or

3 Instructions. TABLE FOR YOUR ANSWERS TO MULTIPLE CHOICE PROBLEMS Indicate by circling directly in the table below your solution to each problem. You may choice up to answers for each problem. The scoring is as follows. For a problem with precisely one answer marked and the answer is correct, 7 points. For a problem with precisely two answers marked, one of which is correct, points. For a problem with precisely three answers marked, one of which is correct, point. All other cases, points. Turn in this Hand In Part of the test. As for the Statement of Mulitple Choice Problem of the exam, note the following. Do NOT hand it in. Take it home with you. Use the back blank sides for scratch paper. Fill in the number of solutions circled column. Your Solutions problem # of solutions circled points a b c d e a b c d e a b c d e 4 4a 4b 4c 4d 4e 5 5a 5b 5c 5d 5e 6 6a 6b 6c 6d 6e 7 7a 7b 7c 7d 7e 8 8a 8b 8c 8d 8e 9 9a 9b 9c 9d 9e a b c d e totol point

4 STATEMENT OF MULTIPLE CHOICE PROBLEMS. Evaluate the integral a. 7 b. 7 c. d.. Evaluate the integral x x 4 + ln + x. a. ln b. ln c. - d.. Evaluate the integral π a. b. c. π d. - π 4. Evaluate the integral π x sinx. sin x cos x. a. 4 7 b. 4 7 c. 5 d Evaluate the integral a. 8 b Evaluate the integral π/4 sec x. a. [ ln + ] b. [ ] ln + c. [ + ln + ] d. [ ] + ln + 6. Evaluate the integral x x c. 5 4 d. x. Recall: ln a + ln b = lnab and ln a ln b = ln a b a. ln b. ln 8. Evaluate the integral c. ln 8 Hint: Do we have strictly bigger bottoms? d. ln x x 4 x x. Recall: ln a + ln b = lnab and ln a ln b = ln a b a. ln b. ln c. ln6 + 6 d. ln Evaluate, if it exists, the integral 4 x x 4. a. ln b. ln 48 c. diverges to d. diverges but not to 4

5 . Let c be a real number. Evaluate, if it exists, the it of the sequence + c n n. n a. b. c c. e c d. e c. 5

Fall 2016 Exam 1 HAND IN PART NAME: PIN:

Fall 2016 Exam 1 HAND IN PART NAME: PIN: HAND IN PART MARK BOX problem points 0 15 1-12 60 13 10 14 15 NAME: PIN: % 100 INSTRUCTIONS This exam comes in two parts. (1) HAND IN PART. Hand in only this part. (2) STATEMENT OF MULTIPLE CHOICE PROBLEMS.