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e105fk - MAC 2311 Exam I and Key Prof S Hudson 1[25pt Short...

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MAC 2311 Sept 28, 2005 Exam I and Key Prof. S. Hudson 1) [25pt] Short answer problems: a) Solve for x , given that log 2 x 3 = 6. b) Given that sec θ = - 5 / 2 and that π/ 2 < θ < π , compute tan θ . c) Solve x 2 - 4 x + 3 < 0. d) State the domain and range of f ( x ) = 2 + x - 3. e) Define instantaneous velocity (I am expecting a short formula with a short explanation). 2) [10pt] Sketch the curve by eliminating the parameter and show the direction of move- ment; x = t , y = 2 t + 4. 3) (15pts) Answer True or False. You do not have to explain. a) tan( π + x ) is continuous at every point in the interval (0 , π ). 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 , δ + < . 001. e) The Earth’s population is a continuous function of time. 4) (25pt) Compute the following limits; a) lim x 3 x 2 - 9 x - 3 = b) lim t 2 - | t - 2 | t - 2 = c) lim x + 5 x 2 +25 x +5 3 x 2 - 75 = d) lim x 3 + π 2 = e) lim x 4 x - 2 x - 4 = 5) [10pt] Answer these using the graph below (it’s based on the first figure on page 121).
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