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15. Let f. g : R → R be continuous at a point c, and let h(x) := sup (f (x). g(x)} for x e R. Show that h(x) = (f(x) + g(x)) + I (x) - g(x)| for all x e R. Use this to show that h is %3D continuous at c.

15. Let f. g : R → R be continuous at a point c, and let h(x) := sup (f (x). g(x)} for x e R. Show that h(x) = (f(x) + g(x)) + I (x) - g(x)| for all x e R. Use this to show that h is %3D continuous at c.

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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15. Let f. g : R → R be continuous at a point c, and let h(x) := sup (f (x). 8(x)} for x € R. Show that h(x) = (f(x) + g(x)} + }If(x) – g(x)| for all x € R. Use this to show that h is continuous at c.
Transcribed Image Text:15. Let f. g : R → R be continuous at a point c, and let h(x) := sup (f (x). 8(x)} for x € R. Show that h(x) = (f(x) + g(x)} + }If(x) – g(x)| for all x € R. Use this to show that h is continuous at c.
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