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Exercise 10: Compute the following limits, using whatever we have learned thus far. If they do not exist, give a short reason why. x1 2 2 a) lim x 1 354 bs b) lim 4x x5 x2x12 2-1 c) lim d) lim x-1 1 I -3 a 3 -) ) 22x 8 e) lim I-4 f) lim 4 IXC 4 4 4 Hint: Note that if limc f(x) L, p > 0, and g(x) = f(x) on (c-p, c)U(c, c+p), then lim c 9(x) = L (in fact, we can pick og = min{p, df} for any e > 0). As an example, if: 9 (x-1)(x-2) IC g(ax) = x -1 then we can let f(x) = x - 2. Then f(x) = g(x), except at x = 1. Therefore, since lim1 f(x) = -1, then lim 1 g(x) = -1. Canider the following functions:

Exercise 10: Compute the following limits, using whatever we have learned thus far. If they do not exist, give a short reason why. x1 2 2 a) lim x 1 354 bs b) lim 4x x5 x2x12 2-1 c) lim d) lim x-1 1 I -3 a 3 -) ) 22x 8 e) lim I-4 f) lim 4 IXC 4 4 4 Hint: Note that if limc f(x) L, p > 0, and g(x) = f(x) on (c-p, c)U(c, c+p), then lim c 9(x) = L (in fact, we can pick og = min{p, df} for any e > 0). As an example, if: 9 (x-1)(x-2) IC g(ax) = x -1 then we can let f(x) = x - 2. Then f(x) = g(x), except at x = 1. Therefore, since lim1 f(x) = -1, then lim 1 g(x) = -1. Canider the following functions:

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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Exercise 10: Compute the following limits, using whatever we have learned thus far. If they do not exist, give a short reason why. x1 2 2 a) lim x 1 354 bs b) lim 4x x5 x2x12 2-1 c) lim d) lim x-1 1 I -3 a 3 -) ) 22x 8 e) lim I-4 f) lim 4 IXC 4 4 4 Hint: Note that if limc f(x) L, p > 0, and g(x) = f(x) on (c-p, c)U(c, c+p), then lim c 9(x) = L (in fact, we can pick og = min{p, df} for any e > 0). As an example, if: 9 (x-1)(x-2) IC g(ax) = x -1 then we can let f(x) = x - 2. Then f(x) = g(x), except at x = 1. Therefore, since lim1 f(x) = -1, then lim 1 g(x) = -1. Canider the following functions:
Transcribed Image Text:Exercise 10: Compute the following limits, using whatever we have learned thus far. If they do not exist, give a short reason why. x1 2 2 a) lim x 1 354 bs b) lim 4x x5 x2x12 2-1 c) lim d) lim x-1 1 I -3 a 3 -) ) 22x 8 e) lim I-4 f) lim 4 IXC 4 4 4 Hint: Note that if limc f(x) L, p > 0, and g(x) = f(x) on (c-p, c)U(c, c+p), then lim c 9(x) = L (in fact, we can pick og = min{p, df} for any e > 0). As an example, if: 9 (x-1)(x-2) IC g(ax) = x -1 then we can let f(x) = x - 2. Then f(x) = g(x), except at x = 1. Therefore, since lim1 f(x) = -1, then lim 1 g(x) = -1. Canider the following functions:
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