Let a > 1. Assume that ap+q = apaq and (ap)q = apq for all p,q
Question:
a) Prove that A(x) exists and is finite for all x ˆŠ R, and that A(p) = ap for all p ˆŠ Q. Thus ax:= A(x) extends the "power of a" function from Q to R.
b) If x, y ˆŠ R with x c) Use Example 2.21 to prove that the function ax is continuous on R.
d) Prove that ax+y = axay, (ax)y = axy, and a-x = 1/ax for all x. y ˆŠ R.
e) For 0
Transcribed Image Text:
A(x) := sup{a": q e Q and q x).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 55% (9 reviews)
a Fix a 1 and for each x R consider the set By the density of rationals there are many q Q such that ...View the full answer
Answered By
Ashington Waweru
I am a lecturer, research writer and also a qualified financial analyst and accountant. I am qualified and articulate in many disciplines including English, Accounting, Finance, Quantitative spreadsheet analysis, Economics, and Statistics. I am an expert with sixteen years of experience in online industry-related work. I have a master's in business administration and a bachelor’s degree in education, accounting, and economics options.
I am a writer and proofreading expert with sixteen years of experience in online writing, proofreading, and text editing. I have vast knowledge and experience in writing techniques and styles such as APA, ASA, MLA, Chicago, Turabian, IEEE, and many others.
I am also an online blogger and research writer with sixteen years of writing and proofreading articles and reports. I have written many scripts and articles for blogs, and I also specialize in search engine
I have sixteen years of experience in Excel data entry, Excel data analysis, R-studio quantitative analysis, SPSS quantitative analysis, research writing, and proofreading articles and reports. I will deliver the highest quality online and offline Excel, R, SPSS, and other spreadsheet solutions within your operational deadlines. I have also compiled many original Excel quantitative and text spreadsheets which solve client’s problems in my research writing career.
I have extensive enterprise resource planning accounting, financial modeling, financial reporting, and company analysis: customer relationship management, enterprise resource planning, financial accounting projects, and corporate finance.
I am articulate in psychology, engineering, nursing, counseling, project management, accounting, finance, quantitative spreadsheet analysis, statistical and economic analysis, among many other industry fields and academic disciplines. I work to solve problems and provide accurate and credible solutions and research reports in all industries in the global economy.
I have taught and conducted masters and Ph.D. thesis research for specialists in Quantitative finance, Financial Accounting, Actuarial science, Macroeconomics, Microeconomics, Risk Management, Managerial Economics, Engineering Economics, Financial economics, Taxation and many other disciplines including water engineering, psychology, e-commerce, mechanical engineering, leadership and many others.
I have developed many courses on online websites like Teachable and Thinkific. I also developed an accounting reporting automation software project for Utafiti sacco located at ILRI Uthiru Kenya when I was working there in year 2001.
I am a mature, self-motivated worker who delivers high-quality, on-time reports which solve client’s problems accurately.
I have written many academic and professional industry research papers and tutored many clients from college to university undergraduate, master's and Ph.D. students, and corporate professionals. I anticipate your hiring me.
I know I will deliver the highest quality work you will find anywhere to award me your project work. Please note that I am looking for a long-term work relationship with you. I look forward to you delivering the best service to you.
3.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Numerical Analysis questions
-
Let X have p.d.f. Prove that the m.g.f. (t) is finite for all t 0 but for no t > 0. if x > 1, x 0 otherwise. f(x) =
-
Let H be a nonempty, closed, bounded subset of Rn. a) Suppose that f : H Rm is continuous. Prove that is finite and there exists an x0 H such that ||f(x0)|| = ||f||H. b) A sequence of functions fk: H...
-
Let E1 be the unit interval [0, 1] with its middle third (1/3, 2/3) removed (i.e., E1 = [0, l/3]U[2/3, 1]). Let E2 be E1 with its middle thirds removed; that is, E2 = [0, 1/9] U [2/9, 1/31 U [2/3,...
-
Make a comparison of the following insurance coverage premium bids and determine from a costing standpoint, which offer is better. Show your calculations: Assume that you, as a risk manager would...
-
McGriff Dog Food Company normally takes 27 days to pay for average daily credit purchases of $9,530. Its average daily sales are $10,680, and it collects accounts in 32 days. a. What is its net...
-
What are the risks of relying on intuition to make decisions? What can a leader do to address these risks and gain the benefits from intuition?
-
Consider two companies with subsidiaries in Venezuela, a country that has been identified as hyperinflationary. U.S. Marts reporting currency is the U.S. dollar, and it uses U.S. GAAP to consolidate...
-
Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residences in the Blacksburg area. The...
-
when you show the workings can you show the excel sheed withformulas on them. this is where i am having the most trouble. Thankyou! Seth Bullock, the owner of Bullock Gold Mining, is evaluating a new...
-
Borges Machine Shop, Inc., has a 1- year contract for the production of 200,000 gear housings for a new off- road vehicle. Owner Luis Borges hopes the contract will be extended and the volume...
-
If f : R R is continuous and prove that f has a minimum on R; that is, there is an xm R such that linoo'f(x) =-imc f(x) = oo, reR
-
For each of the following, prove that there is at least one x R which satisfies the given equation. a) ex = x3 b) ex = 2cos x + 1 c) 2x = 2 - 3x
-
Frevert purchased a new piece of equipment to be used in its new facility. The $370,000 piece of equipment was purchased with a $50,000 down payment and with cash received through the issuance of a...
-
A marketing survey is conducted in which students are to taste two different brands of soft drink. Their task is to correctly identify the brand tasted. A random sample of 180 students is taken....
-
Determine the output of the following 5 C program segments below. You must show all the output. a. int n=1, c=0, a[5]=[9.4,12,1.8); while(n <5) {if (a[n]
-
Why are blacks more likely to receive complications from a public health perspective? How is patient experience a major factor in quality of healthcare services?
-
1. Although cable modems are tested before they are placed in the installer's truck, the installer knows that 30 percent of them won't work properly. The driver must install nine modems today in a...
-
Find the errors in the following code, and make the program be compiled without errors. #include using namespace std; int main() { } int a=20,b=3; float *ptrf, varf =3.14, c=25.0; int num =3, *ptri =...
-
Determine whether f is a rational function and state its domain. f(x) = |x + 1| x + 1
-
What services are provided by the provincial and territorial governments?
-
Determine the mean and variance of the random variable in Exercise 3-15.
-
Determine the mean and variance of the random variable in Exercise 3-17.
-
Determine the mean and variance of the random variable in Exercise 3-19.
-
1. Using the data input provided (Exhibit 1), prepare LAF's master budgets in Excel. Do not hard-code numbers into the spreadsheet, except in the financing section of the cash budget. (1) sales...
-
. Aerodec, Inc., manufactures and sells two types of wooden deck chairs: Deluxe and Tourist. Annual sales in units, direct labor-hours (DLHs) per unit, and total direct labor-hours per year are...
-
. Check n Smith-Kline Company maintains inventory records at selling prices as well as at cost. For 2024, the records indicate the following data: ($ in 000s) Cost Retail Beginning inventory $ 91 $...
Study smarter with the SolutionInn App