Real Analysis Answers

Show that the series 8/(n⁴+x⁴) is uniformly convergent for all real values of x. n=1 to infinity .

Evaluate

lim 3nΣr=1 n^2/(4n+r)^3

n→∞

Find the value of m so that

lim (sin 2x + m sin 3x)/ x^3

x→0

is finite.

Create your own or similar real life situation where rational function is applied

If function f is defined in a sigma- finite measure space.we may choose the function pi n so that each vanishes outside a set of a finite measure.

x is a member of A

Create your own or similar real life situation where rational function is applied

Show that int(A ∩ B) = int(A) ∩ int(B).

Tell whether the following sets A are (i) open or closed, (ii) connected,

(iii) compact. Find (iv) the limit points of A, (v) int(A), (vi) the boundary of A.

A= rational numbers

A = integers