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(Requires calculus)a) Show that if f(x) and g(x) are
Chapter 2, Problem 62E(choose chapter or problem)
Problem 62E
(Requires calculus)
a) Show that if f(x) and g(x) are functions such that f(x) is o(g(x)) and c is a constant, then cf(x) is o(g(x)). where (cf)(x) = cf(x).
b) Show that if f1(x), is f2(x), and g(x) are functions such that f1(x) is o(g(x)) and f2(x) is o(g(x)), then (f1 + f2)(x) is o(g(x)), where (f1 + f2)(x) = f1(x) + f2(x).
Questions & Answers
QUESTION:
Problem 62E
(Requires calculus)
a) Show that if f(x) and g(x) are functions such that f(x) is o(g(x)) and c is a constant, then cf(x) is o(g(x)). where (cf)(x) = cf(x).
b) Show that if f1(x), is f2(x), and g(x) are functions such that f1(x) is o(g(x)) and f2(x) is o(g(x)), then (f1 + f2)(x) is o(g(x)), where (f1 + f2)(x) = f1(x) + f2(x).
ANSWER:
Solution;
Step 1 ;
(a) In this problem given that are function.
and also is
and c is constant.
Then we have to prove that
consider is
Then this can be written as
where
is some constant and also
Multiply both side by constant
.’.
Hence is
for some constant
.