e209k

# e209k - MAC 2311 Exam II and Key AM, Feb 27, 2009 Prof. S....

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MAC 2311 AM, Feb 27, 2009 Exam II and Key Prof. S. Hudson. 1) (5pts each) Calculate the derivative of f (any valid method is OK. If you have simply memorized any of these, include a short note (I reserve the right to check you on this). a) f ( x ) = sin(5 x + 1) b) f ( x ) = x ln( x ) - x c) f ( x ) = tan - 1 ( x ) = arctan( x ) d) f ( x ) = | 3 x | e) f ( x ) = 2 x f) f ( x ) = cos 3 (sin(2 x )) 2) (10pts) Compute the derivative using the deﬁnition (compute a limit): y = 1 /x . 3) (10pts) Find the second derivative, y 00 ( π ), where y = sec(2 x ). 4) (10pts) State the deﬁnition of continuous at x=a . Use this deﬁnition to prove (check) that f ( x ) = x 3 is continuous at x = 2. This should be quick - you can use any known facts about polynomials and limits (no epsilon stuﬀ required). 5) (10pts) Use a local linear approximation to approximate 24. 6) (10pts) A 13 foot ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of

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## This note was uploaded on 05/28/2011 for the course MAC 2311 taught by Professor Staff during the Spring '08 term at FIU.

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e209k - MAC 2311 Exam II and Key AM, Feb 27, 2009 Prof. S....

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