# Math1041ReviewFinalAnswerKey - Math 1041 Section 2.4...

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Math 1041 Answer Key to Final Exam Review Spring 2011 Section 2.4 Preliminary Questions: 2. f (3) = 1 2 Exercises: 20. The function f ( x ) = x - 2 | x - 2 | is discontinuous at x = 2 where it has a jump discontinuity since the one-sided limits as x 2 are not equal (namely, lim x 2 - f ( x ) = - 1 and lim x 2+ f ( x ) = 1). Section 2.5 20. 1 4 Chapter 2 Review Problems 20. 26. 1 9 42. 0 50. b = 7; discontinuous at x = - 2 Section 3.1 53. f ( x ) = x 3 and a = 5. Then the limit is f 0 (5) = 3 · 5 2 = 75. 55. f ( x ) = sin x and a = π 6 . Then the limit is f 0 ( π 6 ) = cos( π 6 ) = 3 2 . Section 3.2 76. The function is discontinuous at x = 1. The function is nondiﬀerentiable at x = 1 because it is discontinuous there and also at x = 2 and x = 3 because the one-sided derivatives at each of these points are not equal to each other. Section 3.7 56. y 0 = t sec( t 2 - 9) tan( t 2 - 9) t 2 - 9 82. d

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## This note was uploaded on 05/07/2011 for the course MATH 1041 taught by Professor Unknown during the Spring '08 term at Temple.

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Math1041ReviewFinalAnswerKey - Math 1041 Section 2.4...

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