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PracticeTest2 - Practice Test#2 Directions Use this...

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Practice Test #2 Directions: Use this practice test as a guide for your study for Test #2. This exam is not comprehensive, so study your class notes and homework problems in addition to completing this exam. Solutions are posted on the course website unde r “Solutions”. 1) Use a graph to find ) 3 ( lim 2 2 x x . Label the limit on your graph. 2) For the function 4 | 4 | ) ( x x x f , do the following: a) Write the function f(x) as a piecewise-defined function. b) Explain in detail why 4 | 4 | lim 4 x x x does not exist. Use a graph in your explanation. c) Find 4 | 4 | lim 7 x x x . Show where this limit is on your graph. 3) For the graph below, find the following: 4) Find 6 6 15 9 6 lim 2 2 1 x x x x . Answer: _________ a) ________ ) 1 ( f b) _________ ) ( lim 1 x f x c) _________ ) ( lim 1 x f x d) _________ ) ( lim 1 x f x e) f(1) = __________ f) _________ ) ( lim 1 x f x g) _________ ) ( lim 1 x f x h) _________ ) ( lim 1 x f x f(x)
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5) If 3 ) ( x x f , find the derivative h x f h x f x f h ) ( ) ( lim ) ( ' 0 . Simplify completely. 6) Find ) 1 3 2 4 ( lim 2 3 x x x x . Answer: __________ 7) Find all horizontal asymptotes of 6 4 1 2 3 ) ( 2 2 x x x x x f using a limit.
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