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Let (an) → 0, and use the Algebraic Limit Theorem to com- pute each of the following limits (assuming the fractions are always defined): (a) lim (13 1+2an 1+3an-4a² (b) lim ((n +2)²-4) an 2+3 (c) lim(+5 an

Let (an) → 0, and use the Algebraic Limit Theorem to com- pute each of the following limits (assuming the fractions are always defined): (a) lim (13 1+2an 1+3an-4a² (b) lim ((n +2)²-4) an 2+3 (c) lim(+5 an

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let (an) → 0, and use the Algebraic Limit Theorem to com- pute each of the following limits (assuming the fractions are always defined): (a) lim 1+2an (1342) 1+3an-4a² (b) lim ((n + 2)²-4) an 2+3 (c) lim+5, an
Transcribed Image Text:Let (an) → 0, and use the Algebraic Limit Theorem to com- pute each of the following limits (assuming the fractions are always defined): (a) lim 1+2an (1342) 1+3an-4a² (b) lim ((n + 2)²-4) an 2+3 (c) lim+5, an
Suppose that (an) is a sequence of nonzero real numbers and that lim an = 0. Compute the following n→∞ limits (you may use the Algebraic Limit Theorem, but clearly state how you are using it and why the hypotheses are satisfied). [For part (a), you may assume that for all n N we have 1 + 3an - 4a2 #0. Similarly, for part (c) you may assume that for all n N we have +30.] an
Transcribed Image Text:Suppose that (an) is a sequence of nonzero real numbers and that lim an = 0. Compute the following n→∞ limits (you may use the Algebraic Limit Theorem, but clearly state how you are using it and why the hypotheses are satisfied). [For part (a), you may assume that for all n N we have 1 + 3an - 4a2 #0. Similarly, for part (c) you may assume that for all n N we have +30.] an
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