# UW-Madison MATH 221 - First Midterm Exam (7 pages)

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## First Midterm Exam

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- Pages:
- 7
- School:
- University of Wisconsin, Madison
- Course:
- Math 221 - Calculus and Analytic Geometry 1

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Name Math 221 First Midterm Exam Thursday October 5 2006 Circle your section 301 302 303 304 305 306 308 310 312 313 7 45 MW 8 50 MW 8 50 MW 9 55 MW 9 55 MW 11 00 MW 12 05p MW 2 25p MW 9 55 11 50 MWF 12 15 2 10 MWF B305 VAN VLECK B333 VAN VLECK B329 VAN VLECK B219 VAN VLECK B105 VAN VLECK B105 VAN VLECK B329 VAN VLECK B203 VAN VLECK 277 BASCOM 3349 ENGR HALL I 40 Points II 40 Points III 35 Points IV 40 Points V 25 Points VI 20 Points Total 200 Points Show your reasoning Murcko Ganguly Andrejko Andrejko Hu Hu Ganguly Murcko Rouse Owen I 40 points In each of the following find dy dx a y sin x b y sin x 1 c y sin x 1 d y sin 1 x II 40 points Find the limit Distinguish between an infinite limit and one which doesn t exist Give reasons sin 6x x 0 x a lim b lim sin 6 x c lim sin 6x x x 0 x sin 6 h sin 6 h 0 h d lim III 35 points Find an equation for the tangent line to the curve x2 xy y 2 1 at the point x y 2 3 IV 40 points State and prove the formula for the derivative of the product of two functions In your proof you may use without proof the limit laws the theorem that a differentiable function is continuous and high school algebra V 25 points a Find f 0 x and g 0 x if f x x 1 x 1 g x x 2 x 2 b Let f x and g x be as in part a and p f g i e p x f x g x Find the derivative p0 x of p x c Let f x and g x be as in parts a and b and let w f g i e w x f g x Find the value g 5 of g u when u 5 and the value w0 5 of the derivative w0 x when x 5 VI 20 points a Draw the graph y f x where f x is the function defined by for x 0 2x 3x for 0 x 1 f x 4x 1 for 1 x b Give a formula like the above formula for f x for the inverse function x f 1 y

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