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Unformatted text preview: MAC 2311 Sept 27, 2006 Exam I and Key Prof. S. Hudson 1) [25pt] Short answer problems: a) Solve for x , given that | x- 1 | < x + 1. b) Solve for x , given that cos(2 x ) = 0. c) Solve for x , given that log 10 (1 + x ) = 3. d) Complete the identity (no explanation required): sin(2 α ) = e) Complete the identity (calculate, using a triangle): sin(cos- 1 x ) = 2) [10pt] Find parametric equations for the portion of the parabola x = y 2 joining (1,-1) to (1,1), oriented upwards. 3) [15pts] Answer True or False. You do not have to explain. a) If f is continuous at 2, then lim x → 2 + f ( x ) exists. 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) ∀ > , ∃ δ > , δ + < . 001. e) A rational function is continuous at every point where the denominator is nonzero. 4) (25pt) Compute the following limits. Notice that 3 are one-sided. You may have to answer, for example, with ‘d.n.e.’ or ‘+ ∞ ’ [the latter will get more credit, if it is correct]....
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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.
- Spring '08