Question

Let ( xn) and (yn) be sequence with xn converge to x and yn converge to...

Let ( xn) and (yn) be sequence with xn converge to x and yn converge to y. prove that for dn=((xn-x)^2+(yn-y)^2)^(1/2), dn converge to 0.
Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove: Let x and y be bounded sequences such that xn ≤ yn for all n...
Prove: Let x and y be bounded sequences such that xn ≤ yn for all n ∈ N. Then lim supn→∞ xn ≤ lim supn→∞ yn and lim infn→∞ xn ≤ lim infn→∞ yn.
If Xn is a cauchy sequence and Yn is also a cauchy sequence, then prove that...
If Xn is a cauchy sequence and Yn is also a cauchy sequence, then prove that Xn+Yn is also a cauchy sequence
Let 0 < θ < 1 and let (xn) be a sequence where |xn+1 − xn|...
Let 0 < θ < 1 and let (xn) be a sequence where |xn+1 − xn| ≤ θn  for n = 1, 2, . . .. a) Show that for any 1 ≤ n < m one has |xm − xn| ≤ (θn/ 1-θ )*(1 − θ m−n ). Conclude that (xn) is Cauchy b)If lim xn = x* , prove the following error in approximation (the "error in approximation" is the same as error estimation in Taylor Theorem) in t:...
Let (X1, Y1), . . . ,(Xn, Yn), be a random sample from a bivariate normal...
Let (X1, Y1), . . . ,(Xn, Yn), be a random sample from a bivariate normal distribution with parameters µ1, µ2, σ2 1 , σ2 2 , ρ. (Note: (X1, Y1), . . . ,(Xn, Yn) are independent). What is the joint distribution of (X ¯ , Y¯ )?
Let {xn} be a non-decreasing sequence and assume that xn goes to x as n goes...
Let {xn} be a non-decreasing sequence and assume that xn goes to x as n goes to infinity. Show that for all, n in N (naturals), xn < x. Formulate and prove an analogous result for a non-increasing sequences.
A generalized numerical method for the initial value problemY′(x) =f(x,Y(x))Y(0) =Y0is given as:yn+1=yn+h[(1−θ)f(xn,yn) +θf(xn+1,yn+1)] (a) Show...
A generalized numerical method for the initial value problemY′(x) =f(x,Y(x))Y(0) =Y0is given as:yn+1=yn+h[(1−θ)f(xn,yn) +θf(xn+1,yn+1)] (a) Show that the numerical method forθ=12is absolutely stable for the modeldifferential equation whenλ <0 . (b) What is the region of absolute stabilty of the numerical method ifθ=13? you can use Elementary Numerical Analysis (3rd Edition) as reference
let Xn be a sequence in a metric space X . If Xn -> x in...
let Xn be a sequence in a metric space X . If Xn -> x in X iff every neighbourhood of x contains all but finitely many points of the terms of {Xn}
) Let α be a fixed positive real number, α > 0. For a sequence {xn},...
) Let α be a fixed positive real number, α > 0. For a sequence {xn}, let x1 > √ α, and define x2, x3, x4, · · · by the following recurrence relation xn+1 = 1 2 xn + α xn (a) Prove that {xn} decreases monotonically (in other words, xn+1 − xn ≤ 0 for all n). (b) Prove that {xn} is bounded from below. (Hint: use proof by induction to show xn > √ α for all...
Find an example of a sequence, {xn}, that does not converge, but has a convergent subsequence....
Find an example of a sequence, {xn}, that does not converge, but has a convergent subsequence. Explain why {xn} (the divergent sequence) must have an infinite number of convergent subsequences.
Let xn be a sequence such that for every m ∈ N, m ≥ 2 the...
Let xn be a sequence such that for every m ∈ N, m ≥ 2 the sequence limn→∞ xmn = L. Prove or provide a counterexample: limn→∞ xn = L.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT