quiz3 - Quiz 1. If f (x) = x2 ex , find f (x). sin(x) 2....

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Unformatted text preview: Quiz 1. If f (x) = x2 ex , find f (x). sin(x) 2. If g (x) = , find g (x). 1 + cos(x) 3. If h(x) = x7 + 3x6 − 5x3 + 2x2 − x + 1, find h (x) and h (x). 4. Find the equation of the tangent line to the curve y = (1 − 2x)100 at the point (0, 1). Solutions 1. f (x) = d d 2x (x )e + x2 ex = 2xex + x2 ex = xex (2 + x). dx dx (1 + cos(x)) d d (sin(x)) − sin(x) (1 + cos(x)) dx dx 2. If g(x)=sin(x) / (1+cos(x)), find g (x) = = (1 + cos(x))2 (1 + cos(x)) cos(x) − sin(x)(− sin(x)) cos(x) + cos2 (x) + sin2 (x) cos(x) + 1 1 . = = = 2 2 2 (1 + cos(x)) (1 + cos(x)) (1 + cos(x)) 1 + cos(x) 3. h (x) = 7x6 + 18x5 − 15x2 + 4x − 1. h (x) = 42x5 + 90x4 − 30x + 4. 4. The slope of the tangent line will be y (0), the value of the derivative at the point (0, 1). y (x) = 100(1 − 2x)99 (−2) = −200(1 − 2x)99 , so y (0) = −200. The equation of the tangent line would be (using point-slope form) y = −200(x − 0) + 1 or simply y = −200x + 1. ...
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This note was uploaded on 02/02/2010 for the course MA 141 taught by Professor Zeck during the Spring '10 term at Quebec Trois-Rivieres.

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quiz3 - Quiz 1. If f (x) = x2 ex , find f (x). sin(x) 2....

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