# WA5 - 10 Y=(2x 3 1 2 Y’ = 2(2x 3 1(6x 2 = 12x 2(2x 3 1 16...

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Robert E Goode MAT-231-GS004 Mentor: Dr. Paoletti 10/01/2011 Writing Assignment #5 Section 3.3 (14,18,20,24,28,32,52,104) and Section 3.4 (10,16,22,30,60,66,102,110,160) Section 3.3 14. f(x) = (x 2 -2x+1)(x 3 -1) f’(x) = (x 2 -2x+1)(3x 2 ) +(x 3 -1)(2x-2) =3x 2 (x-1) 2 +(x 3 -1)(2x-2) =(x-1) 2 (5x 2 +2x+2) f’(0)=0 18. f(x) = sinx/x = sinx* 1/x f’(x) = (xcosx-sinx)/x 2 f’(π/6) = (π/6*√3/2 – ½)/(π 2 /36)= 3√3π-18/π 2 20. f(x)=cosx/e x = cosx* 1/e x f’(x)= e x (-sinx)-cosx(e x )/(e x ) 2 = (-sinx-cosx)/e x f’(0) = -1 24. Y=5/(4x 2 ) Rewrite: Y = (5/4)x -2

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Differentiate: y’= (-5/2)x -3 Simplify: y’= -5/2x 3 28. f(x) = x 3 +3x+2/(x 2 +1) = (3x 2 +3)(x 2 +1)- (x 3 +3x+2)(2x)/(x 2 +1) 2 =x 4 -4x+3/(x 2 +1) 2 32. f(x) = X 1/3 (X 1/2 +3) f’(x)= X 1/3 (1/2X -1/2 )+(x 1/2 +3)(1/3X -2/3 ) f’(x)= 5/6X -1/6 +X -2/3 52. y= xcosx+sinx Y’=-xsinx+cosx+cosx = 2cosx-sinx 104. h(t) = e t sint H’(t)=e t cost+e t sint = e t (cost+sint) H’’(t) =e t (cost+sint) + e t (-sint+cost) = 2e t cos t Section 3.4
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Unformatted text preview: 10. Y=(2x 3 +1) 2 Y’ = 2(2x 3 +1)(6x 2 ) = 12x 2 (2x 3 +1) 16. g(x) = √(5-3x) = (5-3x) 1/2 g’(x)=1/2(5-3x)-1/2 (-3) = -3/(2√(5-3x)) 22. S(t)= (t 2 +3t-1)-1 S’(t)= -(t 2 +3t-1)-2 * (2t+3) = (2t+3)/(t 2 +3t-1) 2 30. Y= ½ X 2 √(16-x 2 ) = 1/2x 2 (16-x 2 ) 1/2 Y’= x*(16-x 2 )+ 1/2X 2 (1/2(16-x 2 )-1/2 (-2x)) =-x(3x 2-32)/(2*√(16-x 2 )) 60. g(t)=5cos 3 πt = 5(cosπt) 3 g’(t) = 15(cosπt) 2 (-sinπt)(π) 66. Y=e-x2 Y’= -2xe-x2 102. f(x) = (x-2)-1 f’(x)=-(x-2)-2 = -1/(x-2) 2 f’’(x)= 2(x-2)-3 110. F(x) = (x 2-3x)-2 F’(x)= -2(x 2-3x)-3 (2x-3) F’(4) = -2(16-12)-3 (8-3) = -5/32 160. Y= 1/3cos12t-1/4sin12t Y’=1/3(-12sin12t)-1/4(12cos12t) =-4sin12t-3cost12t F’(π/8) = -4sin3π/2 – 3cos3π/2 = 4-0=4ft/s=velocity F(π/8) = 1/3cos3π/2-1/4sin3π/2 = ¼ or .25feet...
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WA5 - 10 Y=(2x 3 1 2 Y’ = 2(2x 3 1(6x 2 = 12x 2(2x 3 1 16...

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