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Real Analysis
assume that lim[1+2(-1)^n]Xn = 0. Prove that lim Xn exists and find it.
Real Analysis
show that a nonempty finite set s subsets R contains its supremum
Real Analysis
prove that there exist real numbers which is not algebraic
Real Analysis
for every real numbers which are not algebraic(with proof)
Real Analysis
Let f(x) = |x|^1/2. Is f differentiable at c = 0?
Real Analysis
Q1 If y1<y2 are arbitary real numbers and yn= 1/3yn-1 +yn-2. Show tha <yn> is covergent. what is its limit.
Real Analysis
Which of the following statements are true and why?
1.Any continuous function from the open unit interval (0,1) to itself has a fixed point.
2.logx is uniformly continuous on (1/2,+∞) .
3.If A,B are closed subsets of [0,∞) , then A+B={x+y|x∈A,y∈B} is closed in [0,∞)
4.A bounded continuous function on R is uniformly continuous.
5.Suppose f n (x) is a sequence of continuous functions on the closed interval [0,1] converging to 0 pointwise. Then the integral ∫ 1 0 f n (x)dx converges to 0 .
1.Any continuous function from the open unit interval (0,1) to itself has a fixed point.
2.logx is uniformly continuous on (1/2,+∞) .
3.If A,B are closed subsets of [0,∞) , then A+B={x+y|x∈A,y∈B} is closed in [0,∞)
4.A bounded continuous function on R is uniformly continuous.
5.Suppose f n (x) is a sequence of continuous functions on the closed interval [0,1] converging to 0 pointwise. Then the integral ∫ 1 0 f n (x)dx converges to 0 .
Real Analysis
Using the "E-N" definition of the limit, show that
lim n[(n^2+2)^(1/2) - n] = 1
lim n[(n^2+2)^(1/2) - n] = 1
Real Analysis
Using the "E - N" definition of the limit, show that
lim(3+3/n)^(1/2) = 3^(1/2)
lim(3+3/n)^(1/2) = 3^(1/2)
Real Analysis
Using the "E-N" definition of the limit, show that
lim (2n)/(4n^2+n+1)^(1/2) = 1
lim (2n)/(4n^2+n+1)^(1/2) = 1
