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Unformatted text preview: Exam 2 Math 408C Name
Fall 2008 TA Discussion Time: TTH You must show sufﬁcient work in order to receive full credit for a problem. Do your
work on the paper provided. Write you" name on this sheet and turn it in with your
work. Please write legibly and label the problems clearly. Circle your answers when
appropriate. No calculators allowed. v2 72
1. (14 points) Find all horizontal asyinptotes of f(;r) : if?
.r /
. , _ 1‘ —)— 2
2. (14 ponits)Let ﬂit) : < 1
.r — local extrema. Identify intervals on which f is increasing and those on which f is > . Fnd all critical numbers off and classify the decreasing. 3. (14 points) A retailer has determined that the cost C in dollars of ordering and
. . . . , 2% + 80000 .
storing :13 units of a certain product is (7(1) : W— for 100 g 1" g 300. Find
1.
the order size that will minimize cost. Verify that your solution corresponds to the absolute minimum.) 4. (16 points) Let f(;r) : :L‘ — sinr. lei 0 S '1‘ S 27?. Sketch the graph of the curve
y : ft'r), clearly identifying any local extrema and inﬂection points that exist. You
do not need to ﬁnd the 'r intercepts. 5. (14 points) A particle moves along a coordinate line with acceleration a(t) : l + 3 sin 2‘.
If the initial velocity of the particle is 2 units per second and the initial position is at the origin7 where is the particle after w se‘ onds have passed.7 6. (14 points) A 30 foot ladder is leaning against a 20 foot fence (see sketch below).
The base of the ladder is sliding along ‘lie ground away from the fence at a constant
rate of 2 feet/sec. How fast is the angle between the ladder and the ground changing
at the moment the base of the ladder is 13 feet from the fence? r—v l. (14 points) (a) Use 4 subintervals tr lind upper and lower bounds for the area of the region under the curve 3/ : 412. 1 : .r < 2. «2
(b) Express / 4.172031? as the liinil o i a Riemann sum (do not evaluate).
. 0 Bonus: (/5 points) Right circular cylinoriral cans are to be manufactured to contain
a given volume. There is no waste inwlred in cutting the material for the vertical
sides of the can. but each end piece is to be cut from a square and the corners are wasted. Find the ratio of height to dia ncter for the most economical cans. 1 «dolor
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 Spring '06
 McAdam
 Differential Calculus

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