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166E2-S01

# 166E2-S01 - Z ∞ xe-x 2 dx(b Z 3 1 1 x-1 dx(10 7 Find the...

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MA 166 EXAM 2 Spring 2001 Page 1/4 NAME STUDENT ID RECITATION INSTRUCTOR RECITATION TIME Page 1 /18 Page 2 /30 Page 3 /30 Page 4 /22 TOTAL /100 DIRECTIONS 1. Write your name, student ID number, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes or calculators may be used on this test. Evaluate the integrals in problems 1–5. (6) 1. Z tan 2 x dx (12) 2. Z x + 1 x 3 + x dx

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MA 166 Exam 2 Spring 2001 Name Page 2/4 (12) 3. Z x 3 p 1 + x 2 dx (12) 4. Z p 1 - 4 x 2 dx (6) 5. Z π 2 0 cos 3 x dx
MA 166 Exam 2 Spring 2001 Name Page 3/4 (12) 6. Determine whether each integral is convergent or divergent. Find its value if it is convergent. Important : Show clearly how limits are involved. (a) Z

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Unformatted text preview: Z ∞ xe-x 2 dx (b) Z 3 1 1 x-1 dx (10) 7. Find the length of the curve y = 1 3 ( x 2 + 2 ) 3 2 , 0 ≤ x ≤ 1. (8) 8. Set up an integral for the area S of the surface obtained by rotating the curve y = ln x , 1 ≤ x ≤ 2, about the x-axis. Do not evaluate the integral. S = MA 166 Exam 2 Spring 2001 Name Page 4/4 (12) 9. Consider the lamina bounded by the curves y = x 2 , y = 0, x = 1, and with density ρ = 1. Find the following: (a) The mass m of the lamina. m = (b) The moment M y of the lamina about the y-axis. M y = (c) The moment M x of the lamina about the x-axis. M x = (d) The center of mass (¯ x, ¯ y ) of the lamina. (¯ x, ¯ y ) = (10) 10. Determine whether the sequence converges or diverges. If it converges, ﬁnd the limit. (You need not show work for this problem). (a) a n = cos nπ (b) a n = √ n 1 + n (c) a n = ln n 2 n (d) a n = n sin n n 2 + 1 (e) a n = 3 n 2-2 n + 1 2 n 2 + n-1...
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