Suppose that x R, xn > 0, and xn x as n . Prove

Question:

Suppose that x ∊ R, xn > 0, and xn → x as n → ∞. Prove that √xn → √x as n → ∞. [For the case x = 0, use inequality (8) in Section 1.2.]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 03:55 AM

See More Questions

Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean and known variance 2. In this problem, you will prove the missing steps from the proof that there is...
Suppose that xn R. a) Prove that {xn} is bounded if and only if there is a C > 0 such that |xn| < C for all n N. b) Suppose that {xn} is bounded. Prove that xn/nk 0, as n , for all k N.
Suppose that x and y are extended real numbers and that {xn}, {yn}, and {wn} are real sequences. a) [SQUEEZE THEOREM FOR ]. If xn x and yn x, as n , and xn < wn < yn for n N, prove that wn x as...
For the year ending December 31, Orion, Inc. mistakenly omitted adjusting entries for $1,500 of supplies that were used, (2) unearned revenue of $4,200 that was earned, and (3) insurance of $5,000...
Mel Thomas, the chief financial officer of Preston Resources, has been asked to do an evaluation of Dunning Chemical Company by the president and Chair of the Board, Sarah Reynolds. Preston Resources...
Multiply or divide as indicated. (8y - 16) - - 6 10
ABS Plumbing Ltd wants to prepare flexible budget cost estimates for the following items within a range of 33000 to 41000 chargeable hours. Required (a)Prepare a flexible overhead budget for 33000,...
Sweeten Company had no jobs in progress at the beginning of March and no beginning inventories. The company has two manufacturing departmentsMolding and Fabrication. It started, completed, and sold...
Oslo Company prepared the following contribution format income statement based on a sales volume of 1,000 units (the relevant range of production is 500 units to 1,500 units): Sales Variable expenses...
What are the book to tax differences for the below listed partnership? Also, complete Form 1065. General Information August Easter and Grace Jackson own Notorious B.B.Q. (NB), a limited partnership....
a) Prove Theorem 2.12iv. b) Prove Corollary 2.16.
Prove that given x R there is a sequence rn Q such that rn x as n .
A particle travels along the circular path x 2 + y 2 = r 2 . If the y component of the particles velocity is v y = 2r cos 2t, determine the x and y components of its acceleration at any instant.
What is the area and uncertainty in area of one side of a rectangular wooden board that has a length of ( 2 1 . 4 \ pm 0 . 4 ) cm and a width of ( 9 . 8 \ pm 0 . 1 ) cm ? ( Give your answers in cm 2...
As compared to operating company IPOs, SPAC IPOs are typically a slower process. Group of answer choices True False 2. What is the primary purpose of a SPAC? Group of answer choices To take a company...
A diffraction study of a cubic system with Cu K radiation ( = 0.154 nm) offered the interplanar spacing of a plane, d110 = 2.22 nm. Find out the interplanar spacing of the plane (220), with the aid...
At wood machine. A 20kg box and a 30kg crate are attached to the two ends of a massless string that passes over a massless frictionless pulley. The system is released from rest. Without performing a...
The plastic material placed in front of a lighting instrument to produce colored light is called Group of answer choices a gobo. shutters. a gel. a wrap.
Do you think that one way to comply with the compensation history ban law would be to provide all candidates with a salary range for the job in question and see if they are still willing to continue...
Design an experiment to demonstrate that RNA transcripts are synthesized in the nucleus of eukaryotes and are subsequently transported to the cytoplasm.
Evaluate (-2x) squared and 2x squared when x = 3
(-8x + 5y 12) 6(2x 4y 10)
Evaluate 2x squared when x = 5 and when x = -5
Carmaker produces small cars. As production emits pollution, Carmaker needs to buy pollution permits. It also needs to hire labour. Carmaker's production function is given by: (1) q = min{0.05L,...
Describe the three key differences between the North American Free Trade Agreement (NAFTA) NAFTA and United States-Mexico-Canada Agreement (CUSMA). Support your answer by providing specific examples.
Discuss what is Brexit. Why did the United Kingdom decided to leave the European Union? What is the impact of trade between the U.K. and the E.U. post-Brexit?

Suppose that x R, xn > 0, and xn x as n . Prove

Question:

Step by Step Answer:

Case 1 x 0 Let 0 and choose N so large that n N implies x n 2 ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions