Real Analysis Answers

Find the number of positive and negative roots of the polynomial
P(x) = x3 − 3x2 + 4x − 5. Find P(2) and P′(2) using synthetic division method.

Show that the functions f (x, y) = ln x - ln y and g(x, y) =(x2+2y2)/2xy are functionally dependent.

let S ={(x,y) | x*y=0 } find the limt point

Check whether the set of integers is countable or not.

Prove that a non empty finite set S which is a subset of R contains its infimum

Four relations a to d are defined on sets A and B. Which of the relations represent a function from A to B?.
a. f1 and f2
b.f1 and g1
c. f2 and g1
d. f2 and g2

Let {bn} be a sequence such that bn = 1 + (1/n). Prove that inf(bn) = 1

using delta - epsilon definition prove that lim(x-->0) (sinx/x) = 1