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# Assignment 3 - /x(Hint Use the Squeeze Theorem 2 Find real...

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MATH 137 Assignment 3, Part 2 Due: 11 am, Friday, October 8 Your assignment consists of two separate parts. Part 1 is available online at http://mapleta.uwaterloo.ca and is due at 4 pm on Thursday October 7. Part 2 consists of the problems below plus a MAPLE lab project. Place part 2 of your assignment in the correct drop box outside MC 4066, corresponding to the class section in which you are registered. Hand in your solutions to the following 3 problems plus MAPLE Lab #1. 1. Evaluate the following limits if they exist. (a) lim x 1 - x 3 - 1 | x - 1 | (b) lim x 2 6 - x - 2 3 - x - 1 (c) lim x 0 | x + 1 | - | x - 1 | x (d) lim x 0 x 4 e sin(1
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Unformatted text preview: /x ) (Hint: Use the Squeeze Theorem.) 2. Find real constants a and b such that lim x → √ ax + b-2 x = 1 . (Hint: Since the denominator approaches , the limit must be of type .) 3. Using the ε , δ deﬁnition, prove the following statements. (a) lim x → 2 (5-2 x ) = 1 (b) lim x → 3 ± x 4 + 1 ² = 7 4 (c) lim x → x n = 0 for any positive integer n (Hint: | x n | = | x | n ) Complete MAPLE Lab #1, and attach your printed output, along with your an-swers to any accompanying questions, to the end of this assignment. 1...
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