7. Prove the following comparison theorems for real functions. (a) If f(x) ~ g(x) and g(x) ----;...

Question:

7. Prove the following comparison theorems for real functions.

(a) If f(x) ~ g(x) and g(x) ----; 00 as x ----;

a, then f(x) ----; 00 as x ----; a.

(b) If f(x) :::; g(x) :::; h(x) and L:= lim f(x) = lim h(x), x---+oo x---+oo then g(x) ----; L as x ----; 00.

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: 9780131453333

3rd Edition

Authors: William R. Wade

See More Books

Question Posted: Jul 20, 2024 05:01 AM

See More Questions

Using the symbol M and N, give precise definitions of each expression. lim f(x) = limo f(x) = oo
Prove the following comparison theorems for real functions f and g, and a R. a) If f(JC) > g(x) and g(x) as x a, then f(x) as x a. b) If f(x) then g(x) L as . L:= lim f(x) = lim h(x).
list Evaluate the following integral K dx 2 + 4x + 20 Question 1 Question 2 dx 2 + 4X + 20 tan * + C (Type an exact answer.) O Question 3 O Question 4 O Question 5 Question 6ng thuc chinh... (14)...
Complete the given table. Number of Days Outstanding Accounts Receivable Estimated % Uncollectible Total Estimated Uncollected Accounts 045 days $ 752,000 2 % $enter a dollar amount 4690 days 255,000...
Sumarah Corporation accepted a $ 225,000 two- year note receivable from a customer in connection with a major inventory sale transaction on 1 October 20X5. he note was interest- free, although market...
Consider nodal configuration 4 of Table 4.2. Derive the finite-difference equations under steady-state conditions for the following situations. (a) The upper boundary of the external corner is...
10. X Ltd. belongs to a risk class for which the appropriate price-earnings ratio is 10. It currently has 25,000 equity shares selling at `50 each. The company is contemplating the declaration of `4...
Many companies post their financial statements and auditors report on their home pages, generally under a heading labeled investor relations. Use one of the Internet search engines to do the...
Assume a merchandising company's estimated sales for January, February, and March are $100,000,$120,000, and $110,000, respectively. Its cost of goods sold is always 40% of its Fales. The company...
8. Suppose that f: [a, 00) ----; R for some a E R. Prove that f(x) ----; L as x ----; 00 if and only if f (xn ) ----; L for any sequence Xn E (a, 00) that converges to 00 as n ----; 00.
6. Prove that y'I- cosx/sinx ----; V2/2 as x ----; 0+.
Show your projected income statement. relate changes in the items to your recommendations rather than blindly going with historical percentage changes.
Sketch the Young tableaux for the permutation group $\mathrm{S}_{5}$ and find their dimensionalities using the hook rule.
Boon Lay Trading (Pte) Ltd. is a medium-sized import-export business based in Singapore. As the information systems auditor working on the audit team that is undertaking an audit of Boon Lay, you...
Write a program Potential that creates an array of charged particles from values given on standard input (each charged particle is specified by its $x$ coordinate, $y$-coordinate, and charge...
Ferntree Products Limited (FPL) is a large New Zealand-based manufacturer of diverse products with headquarters in Auckland. It uses information technology extensively to support all aspects of its...
Angela Mica operates the Mica Dance Studio. On June 1, the business's general ledger contained the following information: The following transactions occurred during the month of June: 1 Paid June...
Consider weather conditions for which the prevailing wind blows past the penthouse tower on a tall building. The tower length in the wind direction is 10m and there are 10 window panels. (a)...
Explain how the graph of each function can be obtained from the graph of y = 1/x or y = 1/x 2 . Then graph f and give the (a) Domain (b) Range. Determine the largest open intervals of the domain over...
A health system has forecasted net patient revenue in the first 3 months of the year as follows (figures in millions): January, $200; February, $140; March, $100. Fifty percent of services are...
Assume that no banks hold excess reserves, and the public holds no currency. If a bank sells a $500 security to the Fed, explain what happens to this bank and two additional steps in the deposit...
In the year of his death, L owned a rental property land (FMV $300,000; cost $230,000), building (FMV $380,000; cost $310,000; UCC $220,000). In his Will, he bequeathed the property to his daughter....

7. Prove the following comparison theorems for real functions. (a) If f(x) ~ g(x) and g(x) ----;...

Question:

Step by Step Answer:

An Introduction To Analysis

Students also viewed these Business questions