Let (xn) and (yn) be sequences of positive numbers such that lim(xn/yn) = 0. (a) Show that

Question:

Let (xn) and (yn) be sequences of positive numbers such that lim(xn/yn) = 0.
(a) Show that if lim(xn) = +∞, then lim(yn) = + ∞.
(b) Show that if (yn) is bounded, then lim(xn) = 0.

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

See More Books

Question Posted: Apr 07, 2016 10:56 AM

See More Questions

Let Xn and Yn be independent random variables for all n such that Xn+Yn 0. Prove that there exists a sequence {an}1 CR such that Xn - an , 0. (Hint: consider the medians.)
Let xn x and yn y be convergent sequences in a normed linear space X. The sequence ( xn + yn ) convergent to x + y, and xn converges to x.
Show that if (xn) and (yn) are bounded sequences, then lim sup(xn + yn) < lim sup(xn) + lim sup(yn): Give an example in which the two sides are not equal.
Show that for an integer n > 2, the period of the decimal expression for the rational number is at most n - 1. Find the first few values of n for which the period of - is equal ton- 1. Do you notice...
A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping...
How does an efficient market affect the required and expected rates of return?
State the advantages of a CRSA system for: (a) company managers (b) risk managers (c) internal auditors (d) companies as a whole.
Why would a company prefer a foreign currency option over a forward contract in hedging a foreign currency firm commitment? Why would a company prefer a forward contract over an option in hedging a...
Design a Moore FSM to detect if an input sequence is divisible by 5. Each cycle a new bit comes as input towards LSB (e.g. if the current sequence is '1011' and the input is '0', the new sequence is...
a. Create addition and multiplication tables for base 12 arithmetic. Use alphabetic characters to represent digits 10 and larger. b. Using your tables from part (a), perform the following addition:...
Let (xn) be properly divergent and let (yn) be such that lim(xnyn) belongs to R. Show that (yn) converges to 0.
Investigate the convergence or the divergence of the following sequences: (a) (n2 + 2), (b) (n/(n2 + 1), (c) (n2 + 1/n, (d) (sinn.
F() = sin and g() = cos . Find the exact value of each function below if = 60. Do not use a calculator. g(/2)
Ben's Brewery has a marginal tax rate of 40%. The before-tax cost of debt is 9%. The lease qualifies as a true tax lease for tax purposes. a) Should Ben's Brewery buy or lease the equipment? Show all...
Find the volume of a cylindrical bottle of glue that has a diameter of 5 cm and height of 4.3 cm. Use 3.14 as an approximation for . The volume V of the bottle of glue is (Type an integer or a...
Consider a gas that obeys Bose-Einstein statistics, at a temperature below the Bose-Einstein condensation temperature TBE.
Drive the time independent Schrodinger equation . 1 Explain why we need to use Quantum mechanics instead of .2 classical mechanics Prove mathematically that the total energy is conserved .3 Drive the...
Explain how to cite the following source in your speech. communication Beeney, J. E., Stepp, S. D., Hallquist, M. N., Ringwald, W. R., Wright, A. G. C., Lazarus, S. A., ... Pilkonis, P. A. (2019)....
Nike sports apparel. Identify the type of strategy represented in each statement. A. Differentiation B. Cost leadership C. Focus
10m solution. If Ka(HA) = 10 then pOH of solution will be [Given : log4=0.6] (A) 6.7 (B) Greater than 6.7 & less than 7.0 (C) Greater 7.0 & less than 7.3 (D) Greater than 7.3
Let f(x) be the probability density function for the lifetime of a manufacturer's highest quality car tire, where is measured in miles. Explain the meaning of each integral. a. b. 40,000 f(x) dx...
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2.5 minutes. (a) Find the probability that a customer has to wait more than 4 minutes....
The "Garbage Project" at the University of Arizona reports that the amount of paper discarded by households per week is normally distributed with mean 9.4 lb and standard deviation 4.2 lb. What...
Many American car manufacturers are located in the Southeast. Due to hurricane season, the Southeast has gotten a significant amount of rain, causing vast flooding. How is the supply of cars impacted?
Suppose that the cost in dollars for a weekly production of x tons of sugar is given by the following function (a) Find the marginal cost. 1 C(x) = x+3x+200. (b) Find the cost and marginal cost when...
16. An IEEE standard 32-bit floating point number is N = -15 x 2E-127 x 1.F, where S is the sign bit, F is the fractional mantissa, and E the biased exponent. a. Convert the decimal number 123.5 into...

Let (xn) and (yn) be sequences of positive numbers such that lim(xn/yn) = 0. (a) Show that

Question:

Step by Step Answer:

a There exists N 1 such that if n N 1 then 0 ...View the full answer

Introduction to Real Analysis

Students also viewed these Calculus questions