calc1-exam3s08 - of.2 cm Use differentials to estimate the...

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Math 111 EXAM 3, April 16,2008 Read each problem carefirlly. Show all your work for each problem! Use only the methods discussed in class. No calculators! l. (L2points) Forthe function .A : r|(a - 4, - 1 I r I 4 a) find the critical numbers over the given interval, and b) determine the absolute minimum and absolute marimum values over the given interval. 2. (15 points) Find the following limits: a) tim sxnt!-r b) lim (cscr - cotr) c) fim ( =)" r---+0 ' a---+O\ - c*[\ e / 3. (20 points) For the function U : tr4 + 4e3 + 10 a) find the intervals over which y is increasing or decreasing, b) find the intervals over which gr is concave up or concave down, c) find the local maximum, local mininrum and inflection points (if any), and d) sketch a of the function labeling the points found in c). 4. (14 points) a) Given f (r) : g1, findthe linearization of /(r) about a :81 to find an approximation for (gO)? .
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Unformatted text preview: of .2 cm. Use differentials to estimate the maximum error in the calculation ofthe volume of the cube. What is the relative error and the percentage error? 5- (12points) Aladder L2feet longrestsalongaverticalwall. Ifthebottomoftheladderslides away from the wall at 3 fl/sec, how fast is the angle between the top of the ladder and the wall changing when the angle is f radians? 6. (15 points) Given the frrnctiony : 4 x*l a) find all asymptotes, b) find the local maximum and minimum points (if any), and c) sketch a graph of the function labeling,the asymptotes and the points fotrnd in b). 7. (12 points) A rectangular-box with an open top is to be made from apiece of cardboard with an area of 864rn2 (the total surface area of the open top box). fhe length of the base ofthe box is twice its width. Find the dimensions of the box (length, width and height) that will maximize the volume of the box. Show that your result is a maximum....
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