fall 05 test

fall 05 test - MATH 140 FINAL EXAMINATION, FORM A DECEMBER...

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Unformatted text preview: MATH 140 FINAL EXAMINATION, FORM A DECEMBER 2005 1. Evaluate lim x x 3 cos 2 x . a) The limit does not exist. b) 1 c) 2 d) e) 2. Evaluate lim x 4 sin( x + 3 sin x ). a) 1 b)- 1 c) 4 d) e) 3. Find the slope of the tangent line to the curve y = 5 x 3 at the point (2 , 40). a) lim h 5(2) 3 + 40 h b) lim h 5(2 3- h 3 ) h c) lim h 5(2 + h ) 3- 40 h d) lim h 5 h 3- 40 h e) The slope does not exist. 4. If the tangent line to y = f ( x ) at (8 , 9) passes through the point (5 , 6) find f (8). a) 1 b) 9 c) 2 d)- 1 e) 6 5. If f is a differentiable function, find the derivative of y = x 4 f ( x ). a) 4 x 3 f ( x ) + x 3 f ( x ) b) 4 x 4 f ( x )- x 4 f ( x ) c) 3 x 3 f ( x )- x 4 f ( x ) d) 4 x 4 f ( x )- x 3 f ( x ) e) 4 x 3 f ( x ) + x 4 f ( x ) 6. Differentiate y = sin x 8 + cos x . a) dy dx = 8 cos x- 9 (8 + cos x ) 2 b) dy dx = 8 cos x + 9 (8- cos x ) 2 c) dy dx = 8 cos x + 9 (8 + cos x ) 2 d) dy dx = 8 cos x- 1 (8- cos x ) 2 e) dy dx = 8 cos x + 1 (8 + cos x ) 2 7. If f ( x ) = x p 9- x 2 , find f ( x ). a)- 9 x 9- x 2 b) 9- 2 x 2 9- x 2 c) 1 x 9- x 2 d)- 1 x 2 9- x 2 e) 1 9- x 2 8. If x 4- 7 xy + y 3 =- 5, find dy dx by implicit differentiation at the...
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fall 05 test - MATH 140 FINAL EXAMINATION, FORM A DECEMBER...

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