ReviewProblems_Test1 (3).doc

ReviewProblems_Test1 (3).doc - Review Problems for Test 1...

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Review Problems for Test 1 Calculus I (Math 1600-04) Please make sure that you also review the Classwork Problems 1. For x f = 1 0 0 2 1 0 1 1 2 x x x x , (A) Sketch the function x f y (B) Evaluate the following limits (if the exist): (i) ) ( lim 0 x f x (ii) ) ( lim 0 x f x (iii) ) ( lim 0 x f x (C) Is this function continuous at 1 x , 0 x and 1 x ? Justify your answer using Continuity Test . 2. Evaluate the following limits (if they exist): (a) x h x h h 2 1 2 1 1 lim 0 (b) 15 2 5 4 lim 2 2 5 x x x x x (c) x x x sin lim 2 (d) x x x 3 1 3 1 lim 0 3. For each of the functions below, list all discontinuities (if any), state whether each discontinuity is removable or not and in the case that a discontinuity is removable, define a new function that removes it. (a) 10 3 3 2 x x x y (b) 15 2 6 2 2 x x x x y (c) x y sin 3 ( Make sure you graph x sin to justify your answer ) 4. Evaluate the following limits: (a) 2 5 lim 2 x x (b) x x x x  2 1 2 lim (c) 4 1 lim 2 2 x x (d) x x x x 

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