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49. Show that the function f(x) = y=x² + 3 is continuous for x # 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether ƒ is left-continuous, right- continuous, or continuous at these points (Figure 17). y x² +3 10- x 6x - x² 9. for x < 1 for 1 ≤ x ≤2 for x > 2 y = 10 - x 1 2 FIGURE 17 y = 6x-x² 6 X

49. Show that the function f(x) = y=x² + 3 is continuous for x # 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether ƒ is left-continuous, right- continuous, or continuous at these points (Figure 17). y x² +3 10- x 6x - x² 9. for x < 1 for 1 ≤ x ≤2 for x > 2 y = 10 - x 1 2 FIGURE 17 y = 6x-x² 6 X

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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49. Show that the function f(x) = y = x² + 3 is continuous for x ‡ 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether f is left-continuous, right- continuous, or continuous at these points (Figure 17). 9 x² + 3 10- x 6xx² y for x < 1 for 1 ≤ x ≤ 2 for x > 2 y = 10 - x 1 2 FIGURE 17 y = 6x - x² 6 X
Transcribed Image Text:49. Show that the function f(x) = y = x² + 3 is continuous for x ‡ 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether f is left-continuous, right- continuous, or continuous at these points (Figure 17). 9 x² + 3 10- x 6xx² y for x < 1 for 1 ≤ x ≤ 2 for x > 2 y = 10 - x 1 2 FIGURE 17 y = 6x - x² 6 X
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