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221-angenent-07faex02

# 221-angenent-07faex02 - MATH 221 —— THE SECOND MIDTERM...

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Unformatted text preview: MATH 221 —— THE SECOND MIDTERM November 7, 2007 Your TA: (circle one) Zajj Daugherty Junwu Tu Rachel Davis Derek 'Garton (1) Compute the derivative of each of the following (Show your work). sinx , __ (a) we): Meow =: M)— __ 1+3:2 dy_ (b)y 111(1_\$c)2 =¢ El;— (c) ﬂit) == v 1+6” ==>> NIB) _ ((1) Find the 10th derivative of f 2 62¢ — 6"”2. (2) The function y = f satisﬁes all + y = say/2 for all x. (a) For which value of ac does one have y = 2? ﬂy. (b) Compute d3: When y = 1. (3) An extending ladder is placed against a wall. The angle it makes with the floor is 0 and its length is L. The bottom of the ladder is anchored at a point which is 12 feet away from the wall. When the ladder is 15 feet long, its length is decreasing by 0.5ft/sec. What is the rate of change of the angle 6 at that moment? L( t) 12ft (4) Consider the function f = \/_ — {1/5 ' (a) Find the interva1(s) on which f is increasing. Find the local maxima and minima of f on the interval 0 < a: < oo. _ (b) Find the intervals on which f is convex or concave. Find the inﬂection point(s) in the graph of f. (5) Find the largest value and the smallest value which the functioﬁ v f(:z:) = arcsin(a:) + 2V1 4— 252 can have on the (closed) interval 0 S a: g 1. ...
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