Gateway sample tests

Gateway sample tests - PART VII SAMPLE GATEWAY TESTS 731...

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PART VII SAMPLE GATEWAY TESTS 731

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732 , Differentiation Gateway Test I Name: Instructor: Differentiate, assuming a is a constant. 1. J(x) = (1 + 2x + X3)1/2 2t 2. y = 1+ t2 3. g(t) = at(a + t)4 4. sin(2B+ 5) 5. (y+tr 6. eZ'+z 7. In(xcosx) 8. tan(5 - t2) 9. y-5 5 - y2 10. Find y': e"+Y + x - y2 = 3
733 Solutions to Differentiation Gateway Test I 1 2 + 3x2 1. f'(X)=-{ +2X+X3)-1/2.(2+3x2)= 2 2Vl + 2x + x3 , (1 + t2)(2) - (2t)(2t) 2(1 - t2) 2. Y = (1 + t2)2 = (1+ t2)2 3. g'(t) = at. (4(a + t)3) + a(a + t)4 = 4at(a + t)3 + a(a + t)4 = (a2 + 5at)(a + t)3 d(sin(2B + 5)) 4. dB = cos(2B + 5) .2 = 2 cos(2B + 5) 5. 5 (y + t r . (1 - * ) 2 6. eZ +Z. (2z+ 1) 1 cos x - x sin x 7. -. (1 . cos x - x . sin x) = x cos x x cos x 1 -2t 8. .(-2t)= cos2(5 -t2) cos2(5 - t2) 9 (5 - y2)(1) - (y - 5)(-2y) - yZ- lay + 5 . (5-y2)2 - (5-y2)2 10. eX+Y + x - y2 = 3 eX+Y . (1 + y') + 1- 2y . y' = a y' . (ex+y - 2y) = -ex+y - 1 -ex+y - 1 eX+Y + 1 , - y = eX+Y - 2y - 2y - eX+Y

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734 Differentiation Gateway Test II Name: Instructor: Differentiate, assuming a is constant. 1. y = tan(t2) 1 2. J(x) = 'x2 + a2 3. g(t) = t2et3 4. ytcost 5. 1n(yt) 6. x + sin x x-I 7. esin(2t) 8.~ 9. X2 + 5ax + a2 x 10. Find y' : sin(xy) + y2x = 5
735 Solutions to Differentiation Gateway Test" , 1 ( ) 2t 1. y = ~ ( 2 ) . 2t = cos t , 1 ( 2 2 ) -3/2 -x 2.

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• Fall '14
• Ennis,christopher
• Calculus, Gateway Exam, Mathematical analysis, Logarithm, constant function, Differentiation Gateway Test

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