e106fk - MAC 2311 Exam I and Key Prof S Hudson 1[25pt Short...

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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) > 0 , δ > 0 , 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]. a) lim x 3 + x x 2 - 9 = b) lim x 1 + x 4 - 1 x - 1 = c) lim x →-∞ e x + e - x e x - e - x = d) lim x 0 - e 1 /x = e) lim x 0 x +4 - 2 x = 5) [10pt] Use the method of Ex 1 in Ch 2.1 (use a limit) to find the equation of the tangent
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