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ExtraDiff-Exam1

ExtraDiff-Exam1 - Mathematics 115 F2011 Some Extra Limit...

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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 x 2 + h ( x ), and lim x 2 h ( x ) ?
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