Show that the functions(a) f(x)=1/(1+x2),x∈R, (b) g(x)=x/(1+x2),x∈R, are uniformly continuous, while the functions(c) f(x)=x2,x∈R, (d) g(x)=√∣x∣,x∈R, are not Through graph
Show that the functions(a) f(x)=1/(1+x2),x∈R, (b) g(x)=x/(1+x2),x∈R, are uniformly continuous, while the functions(c) f(x)=x2,x∈R, (d) g(x)=√∣x∣,x∈R, are not Through graph
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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Show that the functions(a)
f(x)=1/(1+x2),x∈R,
(b)
g(x)=x/(1+x2),x∈R,
are uniformly continuous, while the functions(c)
f(x)=x2,x∈R,
(d)
g(x)=√∣x∣,x∈R,
are not
Through graph
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