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211-craciun-07faex02 - Math 211 ~ MIDTERM EXAM 2 — Fall...

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Unformatted text preview: Math 211 ~ MIDTERM EXAM 2 — Fall 2007 YOUR NAME: Circle your TA’s name: Diana Sarb David Seal Holly Chen Jingwei Hu Li Wang Weidong Yin 'Yingzhe Shi Show all your work. Answers without showing all work receive zero points. 1. (10 points) The marginal profit of a company producing .2 units of a product is M P(x) = —0.5:v + 1000. If 20 units are produced and sold, the company’s profit is $10000. What is the profit function P(x)? 2.(20 points) Compute the following indefinite integrals: (a) /t26—tdt 27 varz+3 (b) dt (6) t2+t 1 1 «a +fldzz: (d) / do: (Hint: use the substitutibn u = ’1 + W?) 3. (a) (5 points) Find ‘73 by implicit differentiation if 2y +1ny = 4:133. (b) (10 points) A boat is being pulled toward a pier by a rope attached to a winch (see figure below). Suppose the winch is 7 feet higher than the boat deck, and the rope is being reeled in at a steady rate of 3 feet per minute. How fast is the boat approaching the pier when it is 14 feet away? winch, 4. (10 points) Afarmer has'640 feet of fencing and wants to fence off a rectangular area and divide it into four adjacent sections as shown below. What dimensions will maximize the area? 5.(10 points) Use the fundamental theorem of calculus to compute: (a)/37<t+%) dt 2 (b) /1 glide (c) eZmda: 6. (15 points) Sketch the graph of the function f = $4 — 8x2 + 10. Indicate'any asymptoteS, local or global extreme points, and inflection points. , 7. ( 10 points) Sketch the graph of the function f (t) 2 2t and use formulas from elementary geometry . 3 . (such as: the area of a triangle 2 basexheight/2) to compute the definite integral / 2tdt, Check your ' 1 answer by using the fundamental theorem of calculus. 8.(10 points ) A function whose tangent has slope 2% ~ 3 for each value of 9: passes through the point (0,4). What is the minimum height of its graph? ...
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