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Exam 1 - Fall 2005 - Calculus I Exam#1 Fall 2005 Name Show...

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Calculus I Exam #1 Fall 2005 Name _____________________________ Show all your work on this paper. Solutions without correct supporting work will not be accepted. All solutions must be exact unless stated otherwise in the problem. 1. Use the graph of ) ( x f y = given below to find the limits indicated. (2 points each) a. _____ __________ ) ( lim 2 = - x f x b. _____ __________ ) ( lim 1 = - x f x c. _____ __________ ) ( lim 4 = x f x 2. Evaluate without using a graph or table. (i.e., show that you worked it analytically) (5 pts each) a. 3 lim 2 5 - - x x x = ________________ b. x x x x x 2 2 3 3 lim 2 3 1 + - - = ________________________ c. θ θ θ θ tan cos lim 0 = ________________ d. x x x - - + 2 1 lim 2 = ____________________________ 3. Find all points of discontinuity. Also state which part of the definition of continuity fails at that particular point. If there are none make sure you write ‘NONE” in the blank. (3 points each) a. 3 1 ) ( + - = x x x f Discontinuous at x = _________ Reason: ________________________ Removable or Nonremovable? ________________________ b. - < - = 5 , 11 2 5 , 4 ) ( x x x x x f Discontinuous at x = _________
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