Math 131 Week in Review Sections 2 1 2 5 J Lewis 1 The velocity of an object traveling in a straight line is given by v t 20 t ft sec Find the average acceleration average rate of change of velocity of the object from a t 1 to t 4 sec b from t 4 to t 7 sec v 4 h v 4 Use your calculator to find lim h 0 h 2 Use the calculator to find the limits x a 5 e 1 lim x 0 b x 4 sin x 3 f x ln x 1 1 x lim 2 h 32 h 0 lim f x lim h 0 h 4 h 2 h x 0 0 x e 1 e 1 x Find each limit or state DNE for a c 0 x c c lim x c f x and b c e 1 lim f x x c 2 4 f x x 9 2 x x 6 Find the limits lim x c f x lim x c do not exist a c 3 b c 2 5 Evaluate each limit a lim ln x x 0 b lim x ln x x 0 c lim e x 2 sin x f x lim f x State DNE for any that x c 6 Evaluate each limit 3 a c lim 2 3 8 x 5 x 65 lim x b 2 x 9 x lim 2 8 x 5 x 65 2 x 9 x x x 9x x 2 d lim 5e 7 x 4e x 2 x e lim 5e 7 x 4 e x 2 7 At what x values if any is f not continuous Give a graphical reason and a definition of continuity reason for each discontinuity a b c x2 9 2 x x 6 f x 1 1 sin f x x 1 1 x tan f x x 0 x 3 x 2 x 3 x 2 x 0 x 0 x 0 x 0 x 2 x 1 3 x b 1 x 8 f x a Find the value of b so that f is continuous at x 1 b For the value of b found in part a find the average rate of change of f x from x 0 to x 1 c For the value of b found in part a find the average rate of change of f x from x 1to x 2 d Guess lim h 0 f 1 h f 1 h and f 1 h f 1 lim h 0 9 Find the average rate of change of f x 3 h What do you see in the graph at x 1 x from x 0 to x 1 Does lim h 0 f h f 0 h exist
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