Real Analysis Answers

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

which of the following is not an element of the set of real numbers?

A. √-13 C. 0

B.-6.34 D. 3/7

Assuming you are a researcher tasked to know about some truths in life. You plan to investigate the growth or decay of some things that interest you. You are to report what you have researched and present exponential or logarithmic functions that would model the involved quantities. You also have to present the graph and explain its characteristics or behavior.

Solve 𝑦 ′′ − 𝑥𝑦 ′ + 𝑦 = 0 assuming a power series. Find the range of 𝑥 for which the solution is valid

Check whether the following sets are open sets

a. The set of all rational numbers.

b. Set { 1/n^2 | n∈ N}

Using ∈-δ arguments, prove that

Lim (x^3+1) = 9/8

x→1/2

State the second mean value theorem of integrability. Verify it for the function f and g is defined by f(x)= 6x and g(x)= -5x on [3,4].

Consider the function f defined on R by

f(x)= 2x^3+ 3x^2-72x- 36

In which of the intervals is the function f increasing, and in which of the intervals is f decreasing? Justify your answer

Evaluate

Lim 3nΣr=1 n^2/(4n+r)^3

n→∞