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).

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 .