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Unformatted text preview: MAC 2311 March 1, 2007 Exam II and Key Prof. S. Hudson 1) [40 pts] Compute the derivative, f ( x ) = dy/dx (shortcuts are OK, but show all work); a) f ( x ) = sin( x 3 ) b) f ( x ) = 1 (2 x +1) 3 c) f ( x ) = x +1 x d) f ( x ) = x ln( x )- x e) f ( x ) = | x- 11 | f) f ( x ) = sec( x ) + cot( x ) g) f ( x ) = sin(2 x ) csc( x ) (and simplify - sooner or later) h) x 2 + xy + y 2 = x (use Imp-diff) 2) [10pts] A gas balloon is being filled at a rate of 100 cm 3 of gas per second. At what rate is the radius of the balloon increasing when its radius is 10cm? 3) [10 pts] Match the graph of f in figures (a) thru (d) with the graphs of f in figures (1) thru (5). If the f in figure (a) goes with the f in figure (3), for example, then answer part (a) with a 3 and so on. [Figures were provided on the actual exams, as in problem 23, page 186]. (a) (b) (c) (d) 4) [10 pts] Answer True or False. You do not have to explain....
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