Use the limit definition to prove that if {a n } is a convergent sequence of integers

Question:

Use the limit definition to prove that if {a_n} is a convergent sequence of integers with limit L, then there exists a number M such that a_n= L for all n ≥ M.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 19, 2023 06:28 AM

See More Questions

y The paraboloid is formed by revolving the shaded area around the x axis. Suppose that d = 128 mm and r = 80 mm. The density of the material is p = 5 Mg/m. y = 50x Part A Determine the radius of...
In the figure, lines , m, and n are parallel. What is the value of x + y? A) 160 B) 200 C) 230 D) 290 70 t l m n
Prove that a function converges to at most one limiting value. In other words, use the limit definition to prove that if lim f(x) = L and lim f(x) = L, then L = L. X-C
The Assembly Department of Interface, Inc., manufacturer of computers, had 4500 units of beginning inventory in September, and 8000 units wore transferred to it from the Production Department. The...
Presented below is the December 31 trial balance of New York Boutique. Instructions(a) Construct T-accounts and enter the balances shown.(b) Prepare adjusting journal entries for the following and...
Suggest modifications to the interval-tree procedures to support the new operation INTERVAL-SEARCH-EXACTLY (T, i), where T is an interval tree and i is an interval. The operation should return a...
What is meant by exclusive dealing?
Your analysis of Moen Corporations fixed asset accounts at the end of 2016 reveals the following information: 1. Moen owns two tracts of land. The first, which cost $18,000, is being held as a future...
19.3 Sims Company, a manufacturer of tablet computers, began operations on January 1, 2019. Its cost and sales information for this year follows. $40 per unit $60 per unit $30 per unit $7,000,000...
Determine convergence or divergence using any method covered in the text. 00 n! (2)! n=1
Theorem 1 states that if then the sequence an = (n) converges and Show that the converse is false. In other words, find a function such that a n = (n) converges but does not exist. lim f(x) = L, X-80
What were the social and economic conditions of the entrepreneur prior to the microloan? (pp. 258259)
Task 2 In addition to the report produced for Task 1, the SMT have asked that you produce a short presentation, (minimum of 2 slides per bullet point), to help ensure that employees handle, store and...
Real solutions for x 2 = 5 ( x + 3 6 0 ) ?
1) Two-stage compressor with irreversibilities = You need to build a two-stage compression system with intercooling to increase the pressure of Argon (monatomic gas, constant specific heat) from pi...
A tightrope is connected at each end to a vertical tree trunk at a height of 1.57 meter above the ground. The two trees are located a distance 5.00 meters apart. At the midpoint of the tightrope, a...
A missing order occurs when a maximum of the two-slit diffraction pattern lines up with the minimum of the single slit diffraction pattern. Adjust the parameters of the simulation to create a...
Why are clean rooms so important to microelectronic processing?
The MIT Sloan School of Management is one of the leading business schools in the U.S. The following table contains the tuition data for the masters program in the Sloan School of Management. a. Use...
Which of the following functions are continuous for all values in their domain? Justify your answers. a. a(t) = altitude of a skydiver t seconds after jumping from a plane b. n(t) = number of...
Use a graph to explain the meaning of lim xa + f(x) = - .
Use the graph of f in the figure to find the following values, or state that they do not exist. a. f(-1). b. c. d. e. f(1) f. g. h. i. j. lim_f(x) x-1 lim f(x) r-1+* x-
Arnold inc. is considering a proposal to manufacture high end protein bars used as food supplements by body builders. The project requires an upfront investment into equipment of $1.4 million. This...
Billy Bob bank has three assets. It has $83 million invested in consumer loans with a 3-year duration, $46 million invested in T-Bonds with a 12-year duration, and $69 million in 6-month (0.5 years)...
Ventaz Corp manufactures small windows for back yard sheds. Historically, its demand has ranged from 30 to 50 windows per day with an average of 4646. Alex is one of the production workers and he...

Use the limit definition to prove that if {a n } is a convergent sequence of integers

Question:

Step by Step Answer:

Suppose an converges to L and let 2 Then ther...View the full answer

Calculus

Students also viewed these Mathematics questions