e109pmk

e109pmk - MAC 2311 Exam I 4pm, Jan 30, 2009 Prof. S. Hudson...

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MAC 2311 4pm, Jan 30, 2009 Exam I Prof. S. Hudson 1) [30 points] Compute each limit: a) lim x 2 q 2 x 2 - 8 x - 2 = b) lim x + tan - 1 ( x ) = c) lim x + x 2 - 1 - x = 2) [20pt] Short answer problems: a) Find all values of θ (in radians) that satisfy the equation cos( θ ) = - 1 2 b) Solve x 2 - 4 x + 3 < 0. 3) (20pts) Answer True or False. You do not have to explain. a) tan( π/ 2 + x ) is continuous at every point in the interval (0 ). b) If lim x 2 f ( x ) exists, then lim x 2 + f ( x ) exists. c) If x is a number so that | x - 2 | < 1, then | x - 4 | < 5. d) ± > 0 , δ > 0 + ± < . 001. e) If f (1) = 1 and f (3) = 3, and f is continuous, then f ( x ) = 2 for some x in (1 , 3). f) For f ( x ) = x 2 + 1, the slope of every secant line is positive. g) The domain of f + g is the same as the domain of fg . h) The derivative of tan - 1 ( x ) at x = 1 is positive. i) If
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e109pmk - MAC 2311 Exam I 4pm, Jan 30, 2009 Prof. S. Hudson...

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