MAT 232-Calc-1-A5 - Calculus I Calculus: Early...

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Unformatted text preview: Calculus I Calculus: Early Transcendental Functions , 4th ed., by Ron Larson, Robert Hostetler, and Bruce H. Edwards (Boston: Houghton Mifflin, 2007; ISBN-10: 0-618-60624-6). Written Assignment 5 The written assignment draws on even-numbered exercises from the textbook. Answer all assigned exercises, and show all work. Section Exercises 5.1 6, 10, 12, 32, 38, 54, 56, 70, 74, 80 5.2 2, 10, 16 5.3 6, 28, 44 5.4 10, 14, 18, 28, 32, 38, 40 5.5 14, 30, 52, 56, 62, 88, 92, 102, 106, 110 5.7 6, 8, 20, 30, 54 Section 5.1 6 Find Differential equation & check by differentiation dr / dø = π r = πø + c check: r = πø + c (d / dø) (r) = (d / dø) (πø +c) dr / dø = π 10 Rewrite integrate and simplify ƒ(1 / x 2 )dx rewrite: ƒx-2 dx Integrate: x -1 / -1 +c Simplify: -(1/x) +c 12. ƒx(x 2 +3) dx (multiply it out) rewrite: ƒ(x 3 +3x) dx Integrate: (x 4 / 4) +(3x 2 / 2) + c Simplify: (x 2 / 4) +(x 2 + 6) + c 32 Find the Indefinite Integral & check by differentiation ƒ(t 2 – sin t) dt rewrite: (t 2 – cos t) dt Integrate: (t 3 /3)– cos t +c Check: (t 3 /3)– cos t +c = t 2 – sin t 38 ƒsec y (tan y – sec y) dy rewite: (sec y tan y – sec 2 y) dy Integrate: sec y – tan y +c check: d /dy = sec y – tan y +c = sec y tan y – sec 2 y = sec y (tan y – sec y) 54 dy / dx = 2(x – 1) y’=2(x – 1) calculate out y = ƒ (2x – 2) dx y = (2(x 2 /2) – 2x) dx y = x 2 – 2x +c Points: 3,2 2 = 3 2 – 2(3) +c 2 = 9 – 6 + c 2 = 3 + c 2 – 3 = c-1 = c c = -1 y = x 2 – 2x - 1 56 dy / dx = 3 / x y’= 3 - x y = ƒ (3 - x) dx y = (3x - x 2 /2) +c y = 3 - x + c Points: e, 3 3 = 3(e) – e +c 3 = 3e – e + c 3 = 2e + c 3/2 – e = c c = 3/2 – e y = 3 - x + 3/2 70 Solve differential equation ƒ”(x) = sin x, f’(0) = 1, ƒ(0) = 6 ƒ’(x) = -cos x +c...
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This note was uploaded on 09/29/2010 for the course MAT MAT 231 taught by Professor Hannah during the Spring '10 term at Thomas Edison State.

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MAT 232-Calc-1-A5 - Calculus I Calculus: Early...

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