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1. (a) Let e be some positive number. Show that |r- 4| <+ 13r – 12| < « (b) Assume that g(x) is a function given by 2r? + 3x +2 g(x) - 1² +2 Prove that g(z) is bounded for all |r| < 2. (c) Using the (e- 6) definition, show that f(r) = 3r –1 is continuous at point I= 1.

1. (a) Let e be some positive number. Show that |r- 4| <+ 13r – 12| < « (b) Assume that g(x) is a function given by 2r? + 3x +2 g(x) - 1² +2 Prove that g(z) is bounded for all |r| < 2. (c) Using the (e- 6) definition, show that f(r) = 3r –1 is continuous at point I= 1.

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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1. (a) Let e be some positive number. Show that |r – 4| < + 13r – 12| < e (b) Assume that g(x) is a function given by 2r2 + 3r + 2 g(x) 1² + 2 Prove that g(x) is bounded for all |r| < 2. (c) Using the (e- 8) definition, show that f(r) = 3r -1 is continuous at point * = 1.
Transcribed Image Text:1. (a) Let e be some positive number. Show that |r – 4| < + 13r – 12| < e (b) Assume that g(x) is a function given by 2r2 + 3r + 2 g(x) 1² + 2 Prove that g(x) is bounded for all |r| < 2. (c) Using the (e- 8) definition, show that f(r) = 3r -1 is continuous at point * = 1.
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