2. Consider the functions f(x) g(x): - = 3x2 when x -10 −6 when x = -6' 3x² + 16x 12 x+6 9-x and h(x) A. The graphs of the functions f, g, and ʼn are identical everywhere but the point x = -6. In words, describe the nature of all three of these graphs at points other than x = −6, and then describe the differences in the behavior of these graphs at x = −6. B. Despite the differences in the behavior of these graphs at x = -6, the values of the limits lim_ƒ(x), lim_g(x), and lim_h(x) are all equal. Provide an intuitive explanation to support this statement. (By mentioning the word intuitive, an e- proof is not required. Some other form of support, whether tabular and/or geometric is encouraged instead.) = 3x - 2. 9-1x 9-x
2. Consider the functions f(x) g(x): - = 3x2 when x -10 −6 when x = -6' 3x² + 16x 12 x+6 9-x and h(x) A. The graphs of the functions f, g, and ʼn are identical everywhere but the point x = -6. In words, describe the nature of all three of these graphs at points other than x = −6, and then describe the differences in the behavior of these graphs at x = −6. B. Despite the differences in the behavior of these graphs at x = -6, the values of the limits lim_ƒ(x), lim_g(x), and lim_h(x) are all equal. Provide an intuitive explanation to support this statement. (By mentioning the word intuitive, an e- proof is not required. Some other form of support, whether tabular and/or geometric is encouraged instead.) = 3x - 2. 9-1x 9-x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:2. Consider the functions f(x) =
=
3x 2 when x
-10
3x² + 16x
x + 6
9-x
−6
g(x) =
when x =
A. The graphs of the functions f, g, and h are identical everywhere but the
point x = -6. In words, describe the nature of all three of these graphs at
points other than x = −6, and then describe the differences in the
behavior of these graphs at x = -6.
B. Despite the differences in the behavior of these graphs at a
=
-6, the
values of the limits lim_ƒ(x), lim_g(x), and lim_h(x) are all equal.
Provide an intuitive explanation to support this statement. (By mentioning
the word intuitive, an e-S proof is not required. Some other form of support,
whether tabular and/or geometric is encouraged instead.)
12
, and h(x) = 3x – 2.
-6'
9-x
9-←x
Expert Solution
Step 1
The given functions are , , .
(A) To Explain: The behavior of these function at .
(B) To Find\Explain: the limits of these function at .
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