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Unformatted text preview: Mathematics 115 F2011: Some Extra Limit and Differentiation Problems Do each of the following. Many of the differentiation questions can be solved using the software at http://www.wolframalpha.com/ Sometimes the software gives silly solutions. Do these by hand first and then check with the software. Also, keep in my mind the main differentiation rules you use for these you will need to give your reasoning on the exam. (1) (a) Find lim x 2 x 2- 4 x- 2 (b) Is f ( x ) = x 2- 4 x- 2 continuous at x = 2? Why or why not? Justify. (c) Does lim x 2 x 2 + 4 x- 2 exist? (2) Does lim x 3 1 ( x- 3) 2 exist? (3) Determine lim x - 1- 1 x + 1 . (4) Define the function g ( x ) by the rule: g ( x ) = ( x + 1 if x 2 x 2 if x < 2 What are lim x 2- g ( x ), lim x 2 + g ( x ), and lim x 2 g ( x ) ? For what values of x is g ( x ) continuous at x ? (5) Define the function h ( x ) by the rule: h ( x ) = ( x + 2 if x 2 x 2 if x < 2 (a) What are lim x 2- h ( x ), lim...
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