# WA8 - P(t) = 2/3(150)t 3/2 +500 = 100t 3/2 +500 P(7) =...

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Robert E Goode MAT-231-GS004 Mentor: Dr. Paoletti 10/22/2011 Writing Assignment #8 Section 5.1 (6,10,12,32,38,54,56,70,74,80), Section 5.2 (2,10,16), Section 5.3 (6,28,44) Section 5.1 (6,10,12,32,38,54,56,70,74,80) 6. Dr/d = π R = πθ+C Check d/dθ(πθ+C) =π 10. ᶋ 1/x 2 = ᶋX -2 =x -1 /-1 +C = -1/x +C 32. ᶋ(t 2 -sint)dt=1/3t+cost+C check: d/dt(1/3t 3 +cost+C) = t 2 -sint 38. ᶋ(secy(tany-secy)dy = ᶋ(secytany-sec 2 y)dy =secy-tany+C Check: d/dy(secy-tany+C) =secytany-sec 2 y =secy(tany-secy)

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54. Dy/dx = 2(x-1) = 2x-2, (3,2) Y= ᶋ2(x-1)dx = x 2 -2x+C 2 = (3) 2 -2(3) +C therefore C=-1 Y=X 2 -2x-1 56. Dy/dx = 3/x, X>0, (e,3) Y= ᶋ3/x dx = 3lnx +C 3=3lne +C therefore C=0 Y=3lnx 70. F’’(x) = sinx F’(0) = 1 and f(0) = 6 F’(x) = ᶋsinxdx= -cosx+C 1 F’(0) = -1+C 1 =1 therefore C 1 =2 F’(x) = -cosx+2 F’(x)=-cosx+2 F(x) = ᶋ(-cos+2)dx = -sinx+2x+C 2 F(0) = 0+0+C 2 =6 therefore C 2 =6 F(x) = -sinx+2x+6 74. Dp/dt = K√t, 0<t<10 P(t) = ᶋkt 1/2 dt=2/3kt 3/2 +C P(0) = 0+C=500 therefore C=500 P(1) = 2/3k+500=600 therfore K=150

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Unformatted text preview: P(t) = 2/3(150)t 3/2 +500 = 100t 3/2 +500 P(7) = 100(7) 3/2 +500 = 2352 bacteria F is a mnimum at X=3 80. V = 8ft/s S = 64ft S(t) = -16t 2 +8t=64=0-8(2t 2-t-8)=0 T=(1+65)/4 = 2.266 b. c(t) = -32t+8 = -32(1+65)/4 +8 =-64.498ft/s Section 5.2 (2,10,16) 2. k(k-2) = 3(1) +4(2) +5(3) +6(4) = 50 10. [1-(j/4) 2 ] 16. (2i-3) = 2 i-3(15) = 195 Section 5.3 (6,28,44) 6. Y=3x 2 on (1,3) f(c 1 )x i = f(1+2i/n)(2/n) = 3(1+2i/n) 2 (2/n) =6/n (1+4i/n+4i 2 /n 2 ) =(6/n) (1+4i/n+4i 2 /n 2 ) =6/n[n+(4/n)(n 2 +n)/2) + (4/n 2 )(n 2 +n)(2n+1)/6) =6+(12n+12)/n + 4[(n+1)(2n+1)/n 2 ] 3x 2 dx = lim [6+12(n+1)/n + 4(n+1) (2n+1)/n 2 ) = 6+12+8 = 26 28. A=1/2bh = *8*8 = 32 A = (8-x)dx = 32 44. a. f(x)dx = fx dx - fx dx = 0-5 = -5 b. fx dx - fx dx = 5 +5 = 10 c. 3fxdx = 3fxdx = 3(0) = 0 d. 3f(x)dx = 3fx dx = 3*5 = 15...
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## This note was uploaded on 11/15/2011 for the course MATH 231 taught by Professor Calculusi during the Fall '11 term at Thomas Edison State.

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WA8 - P(t) = 2/3(150)t 3/2 +500 = 100t 3/2 +500 P(7) =...

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