= 1. The graphs of y = 1/x, y = 1/x² and the functions f(x), g(x), h(x), and k(x) are shown in Figure 4.1. (a) Is the area between y = 1/x and y = 1/x² on the interval from x = 1 to ∞ finite or infinite? Explain. (b) Using the graph, decide whether the integral of each of the functions f(x), g(x), h(x) and k(x) on the interval from x = 1 to ∞ converges, diverges, or whether it is impossible to tell. f(x) 1 h(x) Figure 4.1 k(x) 1/x 1/x²
= 1. The graphs of y = 1/x, y = 1/x² and the functions f(x), g(x), h(x), and k(x) are shown in Figure 4.1. (a) Is the area between y = 1/x and y = 1/x² on the interval from x = 1 to ∞ finite or infinite? Explain. (b) Using the graph, decide whether the integral of each of the functions f(x), g(x), h(x) and k(x) on the interval from x = 1 to ∞ converges, diverges, or whether it is impossible to tell. f(x) 1 h(x) Figure 4.1 k(x) 1/x 1/x²
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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Transcribed Image Text:1. The graphs of y = 1/x, y = 1/x² and the functions
f(x), g(x), h(x), and k(x) are shown in Figure 4.1.
(a) Is the area between y = 1/x and y = 1/x² on the
interval from x = 1 to ∞ finite or infinite? Explain.
(b) Using the graph, decide whether the integral of each
of the functions f(x), g(x), h(x) and k(x) on the
interval from x = 1 to ∞ converges, diverges, or
whether it is impossible to tell.
f(x)
1
h(x)
Figure 4.1
k(x)
g(x)
1/x
1/x²
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