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# e107fk - MAC 2311 Exam I Prof S Hudson 1[10pt Sketch the...

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MAC 2311 Sept 25, 2007 Exam I Prof. S. Hudson 1) [10pt] Sketch the curve by eliminating the parameter: x = t + 1, y = t , for 0 t 4. 2) [10pt] Consider the function g graphed in the accompanying figure. For what values of x 0 , - 5 x 0 5, does lim x x 0 g ( x ) exist? 3) [10pt] Find a value for k so that this function is continuous [so, f ( - 2) = lim x →- 2 f ( x )]. f ( x ) = ( x + 2) / ( x 2 - 4) if x = - 2 3 /k if x = - 2 4) (30pt) Compute the following limits. Notice that some are one-sided. You may have to answer, for example, with ‘d.n.e.’ or ‘+ ’ [the latter will get more credit, if both are correct]. a) lim x 0 + ln( x ) = b) lim x + 9 x 2 +16 4 x 2 +25 = c) lim x →-∞ e x + e - x e x - e - x = d) lim x →-∞ 3 e 2 x +1 = e) lim x 0 x +4 - 2 x = f) lim x 1 x 3 - 1 x - 1 = 5) [10pt] Use the method of Ex 1 in Ch 2.1 (use a limit) to find the equation of the tangent line to y = 1 /x at (2,1/2). 6) [20pts] Answer True or False. You do not have to explain. a) If f is continuous at 2, then lim x 2 + f ( x ) exists.

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e107fk - MAC 2311 Exam I Prof S Hudson 1[10pt Sketch the...

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