ASU MAT 265 - mat_265test_1_review_2013 (6 pages)

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mat_265test_1_review_2013

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Pages:
6
School:
Arizona State University
Course:
Mat 265 - Calculus for Engineers I

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MAT265 Review Problems for Exam 1 Domain of a Function review from algebra 1 Find the domain of the following functions a h x x 9 2 b g x 3e x 7 x 2 2 x c f x 15 3x x 2 Properties of a Function review from algebra 2 Determine whether f is even odd or neither a f x cos x b g x 4 x x 3 2 c h x x x Algebra of Functions review from algebra 3 Suppose f x 3x 1 g x x 2 2 x and h x 4e 5 x Find the following a f g 1 b fg 2 c f g x d g f x e f h x f h f x Limit of a Function 2 x 9 at the given numbers correct to six decimal places x 9 Use the results to guess the value of the limit lim f x 4 Evaluate the function f x x 9 x 8 9 8 99 8 999 9 1 9 01 9 001 limit f x x 2 3 if 5 Graph the function f x 3x 1 if 5 2 x if x 1 1 x 2 x 2 Calculate the following a d lim f x b lim f x e x 1 x 2 lim f x c lim f x f x 1 x 2 lim f x x 1 lim f x x 2 if x 2 6 Graph the function g x 3 cos x if x2 if x 0 0 x 2 x 2 Calculate the following a d lim g x b lim g x e x 0 x 2 lim g x c lim g x lim g x f lim g x x 0 x 2 x 0 x 2 Limit Laws 7 Given that lim f x 3 and lim g x 9 evaluate the limit lim x 7 x 7 x 7 8 Algebraically calculate the following limits a 3x 2 10 x 8 x 4 x 2 16 b lim c 3 t 9 t d lim lim x 3 7x 5 4 x 3 2 x 2 x 2 lim t 0 x 2 Squeeze Theorem 7 x 1 9 Use the squeeze theorem to evaluate lim ln x 2 sin x 1 Continuity 10 Explain why each function is discontinuous at the given x value a 5 2 x if f x x 3 if x 2 x 2 b x 2 1 if f x 3 4 x if x 1 x 1 at x 2 at x 1 2 f x 3 x g x f x 11 Find the values for c that will make the function f continuous on cx 2 7 if x 1 f x 2c 4 x if x 1 12 Graph the function f x x then determine the values of for which f is discontinuous Intermediate Value Theorem 13



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