Question

In: Advanced Math

Please follow the comment and solve question 6 and question 7 if you want to get...

Please follow the comment and solve question 6 and question 7 if you want to get thumbs up. Thank you.

6- Let xn ≥0 for all n∈N.

6-1) If xn →0, show that√xn →0.

6-2) If xn →x, show that√xn →√x.

Let A = lim n→∞an. Use an+1 =√2+an, the result of Exercise 6 and limit laws to prove that A = 2.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Solve it step by step and please with clear handwritten. Be ready to follow the comment...
Solve it step by step and please with clear handwritten. Be ready to follow the comment Integrability Topic Question1. Let g : [0, 1] —> R be defined by if x=0, g(x)=1; if x=m/n (m and n are positive integer with no common factor), g(x)=1/n; if x doesn't belong to rational number, g(x)=0 Use the sequential criterion for continuity to prove that g is discontinuous at every rational number in[0,1] Question.2 g is continuous at any irrational point in[0,1]. Explain...
Solve it step by step and please with clear handwritten. Be ready to follow the comment...
Solve it step by step and please with clear handwritten. Be ready to follow the comment Integrability Topic Question1. Let g : [0, 1] —> R be defined by if x=0, g(x)=1; if x=m/n (m and n are positive integer with no common factor), g(x)=1/n; if x doesn't belong to rational number, g(x)=0 Use the sequential criterion for continuity to prove that g is discontinuous at every rational number in[0,1] Question.2 g is continuous at any irrational point in[0,1]. Explain...
Probability question please follow the comment how do we use general inclusion and exclusion theorem to...
Probability question please follow the comment how do we use general inclusion and exclusion theorem to derive 4 to 5 events? for example 3 events are that AUB=A+B-(A intersect B), but how about 4 and 5? Please you need to show me the step rather than paste the inclusion and exclusion formula and explain
Please use c++ and follow the instruction, I really want to fully understand this question and...
Please use c++ and follow the instruction, I really want to fully understand this question and I will use your code to check where I made mistake (Do not skip steps). I have written my own code which has tons of errors, and I am so confused about this lab. I need help. Lab 6.4 – C++ and Functions – Math Test Critical Review A value-returning function is a function that returns a value back to the part of the...
please explain the solution and what it is wrong with my conception. FOLLOW the COMMENT PLEASE...
please explain the solution and what it is wrong with my conception. FOLLOW the COMMENT PLEASE Question: Let A and B are nonempty set bounded subset of R, and let A+B be the set of all sums a+b where a belngs to A and b belongs to B Prove Sup(A+B)=Sup(A)+Sup(B) Solution: Let ε>0, a is in A and b is in B, supA<=a+(ε/2), supB<=b+(ε/2) sup(A + B) ≥ a + b ≥ sup A − ε /2 + sup B...
in c++ please follow instructions and fix the errors and please make a comment next to...
in c++ please follow instructions and fix the errors and please make a comment next to each code error you fix. Below are 25 code fragments, inserted into a try catch block. Each line has zero or more errors. Your task is to find and remove all errors in each fragment. Do not fix problems by simply deleting a statement; repair the problems by changing, adding, or deleting a few characters. There may be different ways to fix them You...
Please follow the instructions and solve it by C++. Thank you! What to Submit Submit the...
Please follow the instructions and solve it by C++. Thank you! What to Submit Submit the following: 1) Your .cpp file of the solution. 2) For what n value (approximately) does your computer stop producing output? Why is this? Enter your answer in the 'Comments' field when you submit the file.   So far in our study of recursion we identified a few common recursive number sequences, such as the Fibonacci numbers. Number sequences like this are not recursive algorithms themselves...
7. (Please, if you are not willing to answer the question completely, please leave the question...
7. (Please, if you are not willing to answer the question completely, please leave the question to someone who is!) a. At the time of his daughter's birth, a man deposited $ 1,000 in an account that pays 6%; this amount is set every birthday. When he turned 12, he increased his appropriations to $ 1,500. Calculate the amount that will be available to her at age 18. b. José earned $ 4,000,000 from the Puerto Rican lotus and will...
7. To get from Earth to Jupiter spacecraft follow the Hohmann Transfer orbit. Using data, you...
7. To get from Earth to Jupiter spacecraft follow the Hohmann Transfer orbit. Using data, you can find online for the orbits of Earth, Jupiter and the Sun (don’t forget to cite it), and assuming that the orbits of Earth and Jupiter are circular with radii equal to their semi-major axes: b. Determine the speed of the spacecraft at the Earth’s orbit in the hohmann transfer orbit? a. Determine the semi-major axis of the Hohmann transfer orbit? c. .Determine the...
Please be able to follow the COMMENT Use induction proof to prove that For all positive...
Please be able to follow the COMMENT Use induction proof to prove that For all positive integers n we have the inequality n<=2^n here is the step: base step: P(1)= 1<=2^1    inductive step: k+1<= 2^(k)+1 <= 2^(k)+k (since k>=1) <= 2^(k)+2^(k) = 2X2^(k) =2^(k+1) i don't understand why 1 can be replaced by k and i don't know why since k>=1
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT