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Unformatted text preview: Math 1110 (Fall 2009) Prelim 1 (09/29/2009) 1 Question 1. (20 points) Please answer the following questions about the function f ( x ) whose graph is shown in the figure below. y=0 y=1 x=0 x=1 (a) Is f ( x ) a one-to-one function? Why or why not? Answer to 1a. No. (b) On which intervals between- 5 and 5 is f ( x ) increasing? Answer to 1b. [- 5,- 1 ] and [ 2,4 ) . (c) For which values of c is lim x c f ( x ) = - 1 ? Answer to 1c. c = . (d) For which values of c is lim x c + f ( x ) 6 = lim x c- f ( x ) ? Answer to 1d. c = - 1 and c = 2 . (e) At which values c between- 5 and 5 is f ( x ) continuous? Answer to 1e. Everywhere except c = - 1,2,4 . Question 2. (18 points) Please evaluate the following expressions, if they exist, or indicate that they do not. If you use a theorem or a fact about limits to help get an answer, be sure to reference it in your solution. If a limit does not exist, indicate in what way it fails to exist. For example, the one-sided limits disagree. (a) lim x 1 x 2- 6x + 5 2x 2- 2 = - 1 (b) lim x - x 2- 6x + 5 2x 2- 2 = 1 2 Math 1110 (Fall 2009) Prelim 1 (09/29/2009) 2 (c) lim x - 1 x 2- 6x + 5 2x 2- 2 = DNE (does not exist) (d) log a ( a 10 ) - log a ( 1 ) = 10 (e) lim...
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This note was uploaded on 03/01/2012 for the course MATH 1110 at Cornell University (Engineering School).