1. (a) Let e be some positive number. Show that|r – 4| < + 13r – 12| < e(b) Assume that g(x) is a function given by2r2 + 3r + 2g(x)1² + 2Prove 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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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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 15BEXP

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Question

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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