242review-part2

242review-part2 - lim x →∞ ln x √ x 2 2d lim x → 1...

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Math 242 Review — Part 2 In addition to (most of) Chapters 6, 7, 11, and 10, we studied the following three “miscellaneous” topics: Newton’s Method (4.8) L’Hopital’s Rule (4.4) Arc Length (8.1) 1. Use Newton’s method with the speciﬁed initial approximation x 1 to ﬁnd x 2 , the next approximation to a solution. 1a. x 3 + 2 x - 4 = 0 , x 1 = 1 1b. x 5 - x - 1 = 0 , x 1 = 1 1c. x 5 = - 2 , x 1 = - 1 1

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2. Evaluate the limits (or show that they don’t exist). 2a. lim x ( π/ 2) + cos x 1 - sin x 2b. lim t 0 e t - 1 t 3 2c.

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Unformatted text preview: lim x →∞ ln x √ x 2 2d. lim x → 1 ln x sin πx 2e. lim x → x-sin x x-tan x 2f. lim x →∞ √ x 2 + 2 √ 2 x 2 + 1 3 2g. lim x → + sin x ln x 2h. lim x →-∞ x 2 e x 2i. lim x → + x x 2 4 3. Find the length of the curve. 3a. y = 1 + 6 x 3 / 2 , ≤ x ≤ 1 3b. x = y 4 8 + 1 4 y 2 , 1 ≤ y ≤ 2 5 3c. y = ln(sec x ) , ≤ x ≤ π/ 4 3d. y = ln(1-x 2 ) , ≤ x ≤ 1 2 6...
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242review-part2 - lim x →∞ ln x √ x 2 2d lim x → 1...

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