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# Purdue MA 23200 - Answers to Even Numbered Exercises

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Answers to Even Numbered ExercisesLesson 1Section 5.426. 528.60815Lesson 2Section 5.58.15ex5+ C10. −12e−t2+ C20. −ln(1 − x) + C24.13sin x3+ C40.124(2 − x4)6+ CLesson 3Section 5.548. −13cos3x + C56.65611664. −e−kb+ 1, or 1 −1ekb70. −2151274. (a) 4, 000, 000e2.475− 1≈ 43, 526, 828(b) 4, 000, 000e2.475− e2≈ 17, 970, 604Lesson 4Section 5.62. xe2x−12e2x+ C4. x sin x − cos x + C10.x4ln x4−x416+ C16.x22+ xln x −x24− x + CLesson 5Section 5.634. 6 ln 6 − 538.10π3−5√3240. 25186942. (a) −e−kTTk+1k2+1k2(b) −75e−2+ 25 ≈ 14.850 mg56. left to the studentLesson 6Section 5.752. 15Lesson 7Section 5.8Calculus for the Life Sciences (Bittinger, Brand & Quintanilla) MA 232 (Fall 2009)Answers to Even Numbered Exercises2. 2π10. π ln 4Lesson 8Section 5.826.3432. 100Lesson 9Section 5.98. divergent28.2e34.Ak36. The area is infinite.Lesson 12Section 7.14. 28, 5, 1214. a)105, b)95Lesson 13Section 7.22. 3(x − y)2, −3(x − y)2, 3, −756. 5, 7, 5, 712. fx= 2ye2xy, fy= 2xe2xy16. fx= 5x4−8xy2+5y3, fy= −8x2y+15xy2−2Lesson 14Section 7.240. fxx= 4e2x−y, fxy= −2e2x−y,fyx= −2e2x−y, fyy= e2x−y46. fxx= 20x3− 8y2, fxy= −16xy + 15y2,fyx= −16xy + 15y2, fyy= −8x2+ 30xy52. 8.2Lesson 15Section 7.32. Relative minimum at−53,1036. Saddle at (0, 0), relative minimum at (2, 2)12. Saddle at (0, 0)Lesson 16Section 7.320. −3.5, no22. Relative minimum at (1, 2)Calculus for the Life Sciences (Bittinger, Brand & Quintanilla) MA 232 (Fall 2009)Answers to Even Numbered ExercisesLesson 18Section 7.52. 18.12e4− e2+12Lesson 19Section 7.522. 760Lesson 20Section 8.14. y = −5 cos x − 4x + C10. y = cos x + x sin x + C24. y = sin x − x cos x + 3Lesson 21Section 8.132. y =14e2x+ 4x +154Lesson 22Section 8.136. Slope is1238. Slope is −2Lesson 25Section 8.24. (−1, 2)8. y =12+Ce4x16. y =sin xx− cos x +CxLesson 26Section 8.232. y = 1 + 3e1t−142. (a) Y0+ kY = 60k(b) Y = 60 − 45ekx(c) k =110ln3945≈ −0.01431(d) 18.11(e) 64.03 pounds per acre48. P (t) = 1 − e−1.2tLesson 27Section 8.32. (a) y = −45(b) unstable(c) none(d) left to the studentLesson 28Section 8.4Calculus for the Life Sciences (Bittinger, Brand & Quintanilla) MA 232 (Fall 2009)Answers to Even Numbered Exercises2. y =3q52x2+ C10. y = ±r3C − 2et3, y = 012.12y2+16y6−12x2= CLesson 29Section 8.422. y =√13e2t− 428. y = −ln3e2− e2t238. (a) left to the student(b) +∞(c) left to the studentLesson 30Section 8.52. (a) y(2) ≈ 0.429(c) y = 4e−xLesson 31Section 6.16.12 −321 −2714.27−6224.8 28 143 27 −25−26 14 −20Lesson 32Section 6.132. (a)0.5 1.250.75 0.25(b)11087(c)164102Lesson 33Section 6.22. x = 10, y = 56. (a, 4a − 2)18. x = 46, y = 18, z = −3234.−8z+115,7z+15, zLesson 34Section 6.226. x = 16, y = 20, z = −628. x = 1, y = 5, z = 542. approximately 113 hatchlings, 42 adultsLesson 37Section 6.36.7/18 −1/182/9 1/9Calculus for the Life Sciences (Bittinger, Brand & Quintanilla) MA 232 (Fall 2009)Answers to Even Numbered Exercises10.−2 2 11 2 00 −1 014.−61 −75 −8121 26 2831 38 41Lesson 38Section 6.326. 4, invertible.30. 0, not invertible.34. −77, invertible.Lesson 39Section 6.42. Eigenvector, with eigenvalue 3.6. Eigenvector, with eigenvalue 10.12. Not an eigenvector.16. v = 5w − 2u.Lesson 40Section 6.422. Eigenvalue r = −1, eigenvector−4t3t,t 6= 0Eigenvalue r = 4, eigenvectort−t, t 6= 0.40.−8181.Lesson 41Section 6.58. xn= c13n+ c25n.16. xn=114(−1)n+1742n.38. xn= −46.105(−0.137)n+ 46.105(0.947)n.Calculus for the Life Sciences (Bittinger, Brand & Quintanilla) MA 232 (Fall

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