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Examen
Math 1242 Final Exam Fall 2010
MATH 1242 FINAL EXAM FALL 2010 PART I (Calculators Not Allowed) Z 1 1. Evaluate the integral (8x − 3) dx. 0 7 (c) 1 3 Z 2 2. Evaluate the integral |3x − 3| dx. (a) 7 9 (b) (d)2(e)3 (d)4(e)5 0 (a) 1 (b) 2 (c) Z 3 1 + cos2 x dx. cos2 x 3. Evaluate the integral (a) 1+tan x+C (b) x+tan x+C Z 2 4. Evaluate the integral 4x ln x dx. (c) x tan x+C(d) x sec x+C (e) x+sec x+C (c)8 ln 2 − 1(d)4 ln 2 − 1(e)4 ln 2 − 2 (c)2e2 − 2e−1(d)2e4 − 2e(e)2e4 − ...
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Examen
Math 1242 Final Exam Spring 2006 Part I (Multiple Choice, No Calculators).
PopularMATH 1242 FINAL EXAM Spring 2006 Part I (MULTIPLE CHOICE, NO CALCULATORS). 1. Compute R 3 2x + − 4 sin x dx. x 2 2 3 2x + − 4 sin x + C x 3 (b) 4x − 2 − 4 cos x + C x 2 (c) x3 + 3 ln |x| − 4 cos x + C 3 2 3 (d) x + 3 ln |x| + 4 cos x + C 3 2 (e) x3 + 3 ln |x| − 2 sin2 x + C 3 1 (a) 2 2. Compute 2 R1 −1 2 xex dx. (a) 2 (b) 2e (c) e 1 1 1 1 (d) e 3 − e− 3 2 2 (e) 0 3. Which of the following definite integrals gives the length o...
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Examen
Math 1242 Final Exam
MATH 1242 FINAL EXAM Spring, 2010 3 7. Which of the following definite integrals gives the length of the curve y = cos(x) for 0 ≤ x ≤ π? Rπ√ (a) 0 1 − cos2 x dx Rπ√ (b) 0 1 + cos2 x dx Rπp (c) 0 1 − sin2 x dx Rπ√ (d) 0 1 + sin2 x dx Rπ√ (e) 0 1 + sin x dx Rx 2 8. If f (x) = 0 et +1 dt, then f 0 (x) = (a) e2x (b) ex 2 (c) ex +1 2 (d) 2xex +1 (e) 2e2x 9. The average value of f (x) = 1 on [1, 5] is 2x + 1 1 (ln 11 − ln 3) 8 1 (b) (ln 11 − l...
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Examen
Math 1242 Final Exam
MATH 1242 FINAL EXAM Spring, 2010 Part II (MULTIPLE CHOICE, CALCULATORS ALLOWED). R1 1. −1 | x | dx = (a) 1/2 (b) −1/2 (c) 0 (d) 1 (e) −1 2. Let an = 2n + 1 for n = 1, 2, 3, . . . . Which of the following statements is true? 4n + 1000 (a) The sequence {an } converges to 0. (b) The sequence {an } converges to 1. (c) The sequence {an } converges to 2. (d) The sequence {an } converges to (e) The sequence {an } diverges. Z 1 3. The improper integral 0 (a) converges to 1....
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Examen
Math 1242 Final Exam
MATH 1242 FINAL EXAM 14. The geometric series 2 + Spring, 2010 5 1 1 1 + + + ··· 2 8 32 (a) diverges. (b) converges to 2. (c) converges to3 . 2 (d) converges to8 . 3 (e) converges to8 . 5 15. The region in the first quadrant bounded by the curves y = x2 , y = 0, and x = 1 is rotated about the x-axis. The volume of the resulting solid is (a)π 5 (b)π 3 (c)π 2 (d) 2 (e) 1 3 16. The velocity, in meters per second, of a particle moving along a straight line is g...
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Examen
Math 1242 Final Exam Spring, 2010
MATH 1242 FINAL EXAM Spring, 2010 4 11. In the Taylor series expansion of f (x) = x4 centered at a = 1, what is the coefficient of (x − 1)3 ? (a) 0 (b) 1 (c) 4 (d) 8 (e) 12 12. The following integral form appears in the Table of Integrals in your text: Z √ u√ 2 a2 u a2 − u2 du = a − u2 + sin−1 + C 2 2 a Z √ 1 − 4x2 dx = Using this form and an appropriate substitution, we obtain x√ 1 1 − x2 + sin−1 x + C 2 2 √ 1 (b) x 1 − 4x2 + sin−1 2x +...
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Examen
Math 1242 Final Exam Spring, 2010
MATH 1242 4. Find R2 0 FINAL EXAM Spring, 2010 2 xex −1 dx. (a) 2e3 (b) 2(e3 − e−1 ) (c) 1 3 (e − e−1 ) 2 (d) 2e4 (e) e3 − e−1 5. Find R x ln x dx. (a) x2 ln x −1 ln x + C 2 (b) x2 ln x +1 ln x + C 2 (c) ln x + C (d)1 1 2 x ln x − x2 + C 2 4 (e)1 2 1 x ln x + x2 + C 2 4 6. The Maclaurin series (Taylor series centered at a = 0) for f (x) = ex is (a) 1 −x2 x4 x6 + − + ··· 2! 4! 6! (b) 1 +x2 x4 x6 + + + ··· 2! 4! 6! (c) ...
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Examen
Math 1242 Final Exam
MATH 1242 FINAL EXAM Part I (MULTIPLE CHOICE, NO CALCULATORS). R2 1. Find 1 4x3 dx. (a) 28 (b) 15 (c) 0 (d) 36 (e) 17 2. Find R 2 cos t dt. (a) −2 sin t + C (b) 2 sin t + C (c) 2 cos t + C (d) −2 cos t + C (e) 2 sin t cos t + C 3. Find (a) 6 (b) 4/3 (c) 2/3 (d) 1 (e) 1/3 R1 0 (2x − 1)2 dx. Spring, 2010 1
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Math 1242 Final Exam Spring 2007
MATH 1242 FINAL EXAM SPRING 2007 PART I (Calculators Not Allowed) 1. Calculate Z 3 sin x + 2x + x dx. (a) − cos x + x + ln | x| + C (b) − cos x + x2 + 3 ln | x| + C x3 3 + +C 3 x 2 (d) − sin x + x + 3 ln | x| + C 3 (e) sin x + 2 − 2 + C x Z π x cos(x2 ) dx. 2. Calculate the definite integral (c) − cos x + 0 (a) 2(sin π)2 sin(π 3 ) 3 cos(π 2 ) (c) 2 sin(π 2 ) (d) 2 (e) sin(π 2 ) (b) 3. Which of the following definite integrals gives the le...
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Examen
Math 1242 Final Exam Part I (Multiple Choice, No Calculators).
MATH 1242 FINAL EXAM Part I (MULTIPLE CHOICE, NO CALCULATORS). ∫2 1. Find 1 x2 dx. (a) 1/3 (b) 2 (c) 7/3 (d) 2/3 (e) 3 2. ∫ (a) 3et dt = ? 3 t+1 e +C t+1 (b) 3et + C (c) et + C (d) 3tet−1 + C (e) 3 ln |t| + C ∫ 4 3. 1 1 du =? u (a) e4 − e1 (b) −3/4 (c) ln(3) (d) ln(4) (e) 3 Fall, 2012 1MATH 1242 FINAL EXAM Fall, 2012 2 2 4. Find the area of the region bounded above by the graph of y = xex and below by the x-axis, 0 ≤ x ≤ 1. (a) 12 e (b) 12...
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Examen
MATH 1242 FINAL EXAM FALL 2011 PART I (Calculators Not Allowed)
MATH 1242 FINAL EXAM FALL 2011 PART I (Calculators Not Allowed) Z 2 (4x − 5) dx. 1. Evaluate the integral −1 (a) −9 (b) Z 4 −5 (c) 1 (d) 5 (e)9 (e)21 |2x − 6| dx. 2. Evaluate the integral 1 (a) −3 (b) 3 Z 1 + sin2 x dx. 3. Evaluate the integral sin2 x (c) 5 (d) 9 (a) 1 + cot x + C (b) x − cot x + C (c) x + cot x + C (d) x + csc x + C (e) x − csc x + C Z 2 4. Evaluate the integral (4x + 1) ln x dx. 1 (a) 7 ln 2 − 1 7 ln 2 − 3 (b) Z 2 ...
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Examen
Math 1242 Common Final Examination Part I
MATH 1242 COMMON FINAL EXAMINATION PART I Name__________________________ Student ID # ____________________ FALL 2008 Instructor:_____________________ Section/Time___________________ This exam is divided into three parts. Calculators are not allowed on Part I. You have three hours for the entire test, but you have only one hour to finish Part I. You may start working on the other two parts of the exam whenever you are done with Part I, but you cannot use your calculator until ALL of th...
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Examen
Math 1242 Final Exam Part I (Multiple Choice, No Calculators).
MATH 1242 FINAL EXAM Part I (MULTIPLE CHOICE, NO CALCULATORS). ∫2 1. Find 1 (2x + 1) dx. (a) 0 (b) 2 (c) 3 (d) 4 (e) 8 2. Find ∫ 2eu du. (a) 2eu + C (b) 2 u+1 e +C u+1 (c) 2 ln u + C (d) 2 cos u + C (e) 0 + C 3. Consider the following graph of a function f : Find ∫2 −1 (a) −1 (b) −1/2 (c) −3/2 (d) 0 (e) 1 f (x) dx. Spring, 2011 1MATH 1242 4. Find ∫1 0 FINAL EXAM (3x − 1)3 dx. (a) 0 (b) 17/12 (c) 9 (d) 5/2 (e) 5/4 5. Find ∫2 1 3 ...
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Examen
Math 1242 Final Exam Part I (Multiple Choice, No Calculators).
MATH 1242 FINAL EXAM Part I (MULTIPLE CHOICE, NO CALCULATORS). R2 1. Find 1 4x3 dx. (a) 28 (b) 15 (c) 0 (d) 36 (e) 17 2. Find R 2 cos t dt. (a) −2 sin t + C (b) 2 sin t + C (c) 2 cos t + C (d) −2 cos t + C (e) 2 sin t cos t + C 3. Find (a) 6 (b) 4/3 (c) 2/3 (d) 1 (e) 1/3 R1 0 (2x − 1)2 dx. Spring, 2010 1MATH 1242 4. Find R2 0 FINAL EXAM Spring, 2010 2 xex −1 dx. (a) 2e3 (b) 2(e3 − e−1 ) (c) 1 3 (e − e−1 ) 2 (d) 2e4 (e) e3 − e−1 5. F...
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Examen
Math 1242 Final Exam Fall 2010
MATH 1242 FINAL EXAM FALL 2010 PART I (Calculators Not Allowed) 1. Evaluate the integral Z 1 0 (8x − 3) dx. (a) 7 9 (b) 7 3 (c) 1 (d) 2 (e) 3 2. Evaluate the integral Z 2 0 |3x − 3| dx. (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 3. Evaluate the integral Z 1 + cos2 x cos2 x dx.
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