Numerical Analysis

prove Show that (5,3)^R + (2,5)^R = (5,6)^R.

Integers

Show that (+2) + (-3) = (-1).

natural number

prove If n is a natural number, then (n,2n)^R = -n

Prove that the product of two postive intergers is a postive interger.

Prove that the product of two postive intergers is a postive interger.

Sequences and limits

establish the convergence and find the limits of the following sequences ((1+1/2n)^n)) ((1+1/n^2)^(2(n^2))) ((1+2/n)^n)) Give an example of a convergent sequence Xsubn of positive numbers with lim(Xsubn^1/n)=1 Give an example of a divergent sequence Xsubn os positive numbers with lim(Xsubn^1/n)=1

Sequence and series

for Xsubn given by formulas establish either the convergence or the divergence of the sequence X=Xsubn Xsubn= n/(n+1) Xsubn= 2n^2+3/(n^2+1) find the limits of the following sequences: lim((2+ 1/n)^2)) lim((-1)^n/(n+2)) lim((n^1/2)-1)/((n^1/2)+1)) lim((n+1)/(n(n^1/2))) establish the convergence and find the limits o ...continues

Chaucy

Prove that every chaucy sequence is bounded

Continuity

suppose f : (a,b)->R is continuous and f(r)=0 for each rational number r in(a,b) prove that f(x)=0 for all x in (a,b)

Algebra of derivatives

Suppose f :R->R is differentiable and define g(x)=x^2f(x^3). show that g is differentiable and compute g'

Positive number proof

prove that the sum of two positive integers is a positive number using the some New Notation information on the attached document