Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) = − 3x + 2, and h(x) = mx + b. A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (-1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. D. Within the context of the e-8 definition of a limit, your result from part B suggests that if € is equal to 2, the largest that can be chosen for function g(x) is 6. Explain. E. The following statement is (ever so slightly) false: "Within the context of the e-8 definition of a limit, the results from parts B and C suggest that for a given positive real number €, the largest that can be chosen for function h(x) is" Modify this statement (ever so slightly) so that it is true, and
Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) = − 3x + 2, and h(x) = mx + b. A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (-1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. D. Within the context of the e-8 definition of a limit, your result from part B suggests that if € is equal to 2, the largest that can be chosen for function g(x) is 6. Explain. E. The following statement is (ever so slightly) false: "Within the context of the e-8 definition of a limit, the results from parts B and C suggest that for a given positive real number €, the largest that can be chosen for function h(x) is" Modify this statement (ever so slightly) so that it is true, and
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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Just need help with Questions D and E. Thank you so much.
Transcribed Image Text:4. Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) x + 2, and h(x)
A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain.
B. If function g has a codomain of (-1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain.
C. Within the context of the €-
f(x) is 1. Explain.
D. Within the context of the e- definition of a limit, your result from part B suggests that if € is equal to 2, the largest that can be chosen for function
g(x) is 6. Explain.
E. The following statement is (ever so slightly) false: "Within the context of the e- definition of a limit, the results from parts B and C suggest that for a
given positive real number €, the largest that can be chosen for function h(x) is!" Modify this statement (ever so slightly) so that it is true, and
S
briefly describe why the e-6 definition of a limit demands such a modification be applied.
=
= mx + b.
definition of a limit, your result from part A suggests that if € is equal to 2, the largest that & can be chosen for function
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