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

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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
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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
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ƒ’(x) = -cos x +c 1 ƒ’(0) = 1 ƒ’(0) = -1 + c 1
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