242sugprob8 - 11 12a Find the length of the curve y = 2 x 3...

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Math 242 Suggested lab/discussion problems, Oct 25 and 27 This is a longer list of problems than usual. It can also serve as practice for Test 2. 1a. Evaluate Z π/ 2 0 cos 3 x dx . 1b. Evaluate Z π/ 2 0 cos 2 x dx . 1
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2. Evaluate Z sec 3 x dx . 2
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3. Evaluate Z 2 1 x 2 - 1 x dx . 3
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4. Evaluate Z x 3 x 2 + 100 dx . 4
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5. Evaluate Z 1 / 2 0 1 + 4 x 2 dx . (Hint: At some point, you may want to use the answer from an earlier question.) 5
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6. Evaluate Z 1 x 2 - 49 dx . 6
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7. Evaluate Z x - 9 ( x + 5)( x - 2) dx . 7
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8. Use Newton’s method to approximate the square root of 2. Use the initial approximation x 1 = 1, and use two iterations of Newton’s method. 8
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9. Use the Trapezoid Rule and Simpson’s Rule, with n = 4 subintervals, to estimate Z π 0 sin x dx . 9
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10. Evaluate Z 1 1 (3 x + 1) 2 dx , or show that it diverges. 10
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11. Evaluate Z -∞ x 1 + x 2 dx , or show that it diverges.
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Unformatted text preview: 11 12a. Find the length of the curve y = 2 x 3 / 2 between x = 0 and x = 7. 12b. Find the length of the curve y = x 2 between x = 0 and x = 1 / 2. 12 13. For each of the following series, determine whether it is convergent or divergent. Give reasons. 13a. ∞ X n =0 1 ( √ 2) n 13b. ∞ X n =1 (-3) n-1 4 n 13 13c. ∞ X k =2 k 2 k 2-1 13d. ∞ X n =1 arctan n 14 13e. ∞ X n =1 1 n 1 / 5 13f. ∞ X n =1 1 n 5 15 13g. ∞ X n =1 1 (2 n + 1) 3 13h. ∞ X n =1 1 √ n + 4 16 13i. ∞ X n =1 ne-n 13j. ∞ X n =1 1 n 3 + n 17 13k. ∞ X n =1 n + 1 n √ n 13l. ∞ X n =1 9 n 3 + 10 n 18...
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