HW2 - etc or the names of the laws(sum law di ff erence law etc lim x → 1 ± 1 3 x 1 4 x 2 3 x 4 ² 3 2 2.3 10(a What is wrong with the

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M408C, Homework 2 Insturctor: Guoliang Wu Due: Wednesday, September 8 1 Reading assignment Please finish reading Chapter 1 and Appendices A–E, by the end of this week. 2 Problems on Quest Please visit Quest https://quest.cns.utexas.edu/ , click on “Get Started”, log on with your UT EID, and answer the questions online. If you have any questions regarding Quest, please let me know. The deadline for this part is Wednesday 4PM. After that the system will not allow you to do the homework. 3 Problems from textbook Youneedtoturninyouranswerstothequestionsinthispart atthebeginningof the discussion section on Thursday (9 / 9) . Explain your work! Correct answers alone are not enough. 1. ( § 2.3, #7) Evaluate the limt and justify each step by indicating the appro- priate limit law(s). You can use the numbering in the textbook (Law 1, 2,
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Unformatted text preview: etc.) or the names of the laws (sum law, di ff erence law, etc.) lim x → 1 ± 1 + 3 x 1 + 4 x 2 + 3 x 4 ² 3 2. ( § 2.3, # 10) (a) What is wrong with the following equation? x 2 + x-6 x-2 = x + 3 1 (b) In view of part (a), explain why the equation lim x → 2 x 2 + x-6 x-2 = lim x → 2 ( x + 3) is correct. 3. ( § 2.4, #19) Prove the statement using the ε,δ function of limit. lim x → 3 x 5 = 3 5 . Hint: Mimic Example 2 on P90. 4. ( § 2.5, #17) Explain why the function is discontinuous at the given number a . Sketch the graph of the function. f ( x ) = 1-x 2 if x < 1 1 / x if x ≥ 1 , where a = 1 . 2...
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This note was uploaded on 12/03/2010 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas at Austin.

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HW2 - etc or the names of the laws(sum law di ff erence law etc lim x → 1 ± 1 3 x 1 4 x 2 3 x 4 ² 3 2 2.3 10(a What is wrong with the

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