Question

In: Advanced Math

Analysis Integral confused concept. Please clear writing and follow the comment 1. upper sum with respect...

Analysis Integral confused concept. Please clear writing and follow the comment

1. upper sum with respect to P is U(f,P)= sum of Mk(xk-xk-1). Does that equal to U(f)=inf{u(f,P): p is a element of Q} (Q is the collection of all possible partition})

Also, is Mk=sup{f(x):x is a element of {xk-1,xk}?????

2. If Q is a refinement of P, then U(f, Q)<=U(f, P) and L(f, P),<=L(f,Q). I don't understand the geometric meaning behind this because Q has more element than P and contains all of the elements from P, However, why U(f, Q)<=U(f, P)????

This Q is not the Q from question1

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Conception about Integral, lower sum, upper sum.. Clear writing please and follow the comment What is...
Conception about Integral, lower sum, upper sum.. Clear writing please and follow the comment What is the difference between lower sum and lower integral by the textbook, lower sum is defined by the infimum but lower inegral is using supremum? how come? Please explain. By the Real analysis
Solve it step by step and please with clear handwritten. Be ready to follow the comment...
Solve it step by step and please with clear handwritten. Be ready to follow the comment Integrability Topic Question1. Let g : [0, 1] —> R be defined by if x=0, g(x)=1; if x=m/n (m and n are positive integer with no common factor), g(x)=1/n; if x doesn't belong to rational number, g(x)=0 Use the sequential criterion for continuity to prove that g is discontinuous at every rational number in[0,1] Question.2 g is continuous at any irrational point in[0,1]. Explain...
Solve it step by step and please with clear handwritten. Be ready to follow the comment...
Solve it step by step and please with clear handwritten. Be ready to follow the comment Integrability Topic Question1. Let g : [0, 1] —> R be defined by if x=0, g(x)=1; if x=m/n (m and n are positive integer with no common factor), g(x)=1/n; if x doesn't belong to rational number, g(x)=0 Use the sequential criterion for continuity to prove that g is discontinuous at every rational number in[0,1] Question.2 g is continuous at any irrational point in[0,1]. Explain...
Mathematics real analysis(please follow the comment) Theorem: There exists a unique positive real number a is...
Mathematics real analysis(please follow the comment) Theorem: There exists a unique positive real number a is in R, satisfying a^2=2 Please proof it. Hint(you need to prove Uniqueness and Existence. For Existence(you need to let a=supA and prove contradicts a^2<2, a^2>2 also use the Archimedean property) Show every steps. Use contradiction proof
Prove that step by step and clear handwritten. Follow the comment Conception: Limit point 1.Prove N'=empty...
Prove that step by step and clear handwritten. Follow the comment Conception: Limit point 1.Prove N'=empty 2.Prove Q'=R 3. E=(2,5), E'=[2,5] my question is that why the collection limit point of E includes 2 and 5? obviously, 2 and 5 are not in E. If they can be limit point in E does that mean R can be all set's collection of all limit point? such as R'=R, Q'=R, N'=R???
Explain the concept of benchmarking with respect to the analysis and interpretation of profit. Discuss the...
Explain the concept of benchmarking with respect to the analysis and interpretation of profit. Discuss the advantages and disadvantages of the different ways of monitoring profit.
please explain the solution and what it is wrong with my conception. FOLLOW the COMMENT PLEASE...
please explain the solution and what it is wrong with my conception. FOLLOW the COMMENT PLEASE Question: Let A and B are nonempty set bounded subset of R, and let A+B be the set of all sums a+b where a belngs to A and b belongs to B Prove Sup(A+B)=Sup(A)+Sup(B) Solution: Let ε>0, a is in A and b is in B, supA<=a+(ε/2), supB<=b+(ε/2) sup(A + B) ≥ a + b ≥ sup A − ε /2 + sup B...
in c++ please follow instructions and fix the errors and please make a comment next to...
in c++ please follow instructions and fix the errors and please make a comment next to each code error you fix. Below are 25 code fragments, inserted into a try catch block. Each line has zero or more errors. Your task is to find and remove all errors in each fragment. Do not fix problems by simply deleting a statement; repair the problems by changing, adding, or deleting a few characters. There may be different ways to fix them You...
GIVE A DEFINITION. PLEASE BE CLEAR OF WHICH YOU ARE DEFINING BY WRITING THE WORD NEXT...
GIVE A DEFINITION. PLEASE BE CLEAR OF WHICH YOU ARE DEFINING BY WRITING THE WORD NEXT TO THE DEFINITION INFERENTIAL STATISTICS OBSERVATIONAL STUDY EXPERIMENTAL STUDY DESCRIPTIVE STATISTICS DISCRETE VARIABLES CLUSTER SAMPLING STATISTIC SAMPLE CONVENIENCE SAMPLING RANDOM SAMPLING STRATIFIED SAMPLING MULTISTAGE SAMPLING QUANTITATIVE DATA QUALITATIVE DATA PARAMETER POPULATION
Please clear writing and explain step by step this should be a simple question Consider the...
Please clear writing and explain step by step this should be a simple question Consider the function f : [0,1]→R defined by (f(x) =0 if x = 0) and (f(x)=1 if 0 < x≤1) (i)Compute L(f) andU(f). (ii) Is f Riemann integrable on [0,1]?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT