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
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: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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