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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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 Fall '06
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 Calculus, Derivative, Fundamental Theorem Of Calculus, Winch

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