Problem 21 Take functions f.g; each of them maps interval [a, b] to R. Let ro € (a, b). Show that if lim-ro h(r) = 0 and g is bounded, then limo (g(x)h(x)) = 0. Does the same hold if we change the 0 to another value, i.e. assume lim-, h(x) = c/0 instead of lim-roh(x)=0?
Problem 21 Take functions f.g; each of them maps interval [a, b] to R. Let ro € (a, b). Show that if lim-ro h(r) = 0 and g is bounded, then limo (g(x)h(x)) = 0. Does the same hold if we change the 0 to another value, i.e. assume lim-, h(x) = c/0 instead of lim-roh(x)=0?
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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Take functions f, g; each of them maps interval [a, b] to R. Let to € (a, b).
Show that if lim-ryh(x) = 0 and g is bounded, then lim (g(x)h(x)) = 0. Does the same hold
if we change the 0 to another value, i.e. assume limo h(r) = c#0 instead of lim-roh(x)=0?
2-20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47456ed3-eb8f-43e4-a5c7-fb8562737ff3%2F81fc4029-81c6-45c2-b0cb-22dbcb8304e5%2Fkn31c0i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem
Take functions f, g; each of them maps interval [a, b] to R. Let to € (a, b).
Show that if lim-ryh(x) = 0 and g is bounded, then lim (g(x)h(x)) = 0. Does the same hold
if we change the 0 to another value, i.e. assume limo h(r) = c#0 instead of lim-roh(x)=0?
2-20
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