Real analysis. Please solve all questions
thank you
Homework Answers
![Af6 1(a). Let a=Xo <X, LX, ... .? Xn- be a partition on [a, b] are Caset. Now suppose that partition contains the points e 4](http://img.homeworklib.com/questions/31d39d50-f6e3-11eb-aca4-d9dc4ae07e18.png?x-oss-process=image/resize,w_560)
Add Answer to:
Real analysis. Please solve all questions
thank you
1. Let h be a positive real number,...
2. Let a be a positive real number, let r be a real number satisfying r...
2. Let a be a positive real number, let r be a real number satisfying r >1, let N be an integer greater than one, and let tR -R be the integrable simple function defined such that tr,N(r) = 0 whenver x < a or z > ar*, tr,N(a) = a-2 and tr,N(z) = (ar)-2 whenever arj-ıく < ar] for some integer j satisfying 1 < j < N. Determine the value of JR trN(x) dz.
Real Analysis question, give clear writing please Let h(x) be the function on (0, 1) defined...
Real Analysis question, give clear writing please
Let h(x) be the function on (0, 1) defined by ſi x <1 h(x) = 2 X=1 (a) For any P, what is the value of L(f,P)? (b) Can you find a P such that U(f,P) is within 1/10 of L(f,P)? (c) Show that h is integrable.
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that t...
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
1. Let p be a positive real number with 0 < p < 1, and let...
1. Let p be a positive real number with 0 < p < 1, and let ni, N2, N3 be positive integers. Sup- pose that Xı has a Bin(ni,p) distribution, X2 has a Bin(n2, p) distribution, and X3 has a Bin(n3, p) distribution. Show that the random variable Z = X1 + X2 + X3 also has a binomial distribution, and find the parameters of that distribution.
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we ...
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we would like to show that for all 0 SjSk-, the function satisfies the advancement operator equation (A -r)f0 (a) Show that this is true whenever J-0. You can use the fact that f(n) = crn satisfies (A-r)f = 0. (b) Suppose fm n) satisfies the equation when m s k-2 for every choice of c. Show that )...
Let α and β be real numbers with 0 < α < βく2m and let h...
Let α and β be real numbers with 0 < α < βく2m and let h : [α, β] → R>o be a continuous function that is always positive. Define Rh,a to be the region of the (x,y)-plane bounded by the following curves specified in polar coordinates: r-h(0), r-2h(0), θ α, and θ:# β. 3. (a) Show that (b) (c) depends only on β-α, not on the function h. Evaluate the above integral in the case where α = π/4...
Please do 10 & 11 Use Intermediate Value Theorem lial p(x) = x4 +7x = 9...
Please do 10 & 11
Use Intermediate Value Theorem lial p(x) = x4 +7x = 9 has two real root. 8. df Open with Google Docs Then use your calculator to find the ro 9 Let f(z)2with € [0, 00). Find a positive mumber e and two sequences {xn} and {yn} such that lim-(nn) = 0 but |f(xn)- f(Yn)| 2 e. Then conclude that f(x) = x2 is not uniformly continuous on [0, ao) [0, oo). Show that f is...
1. Let {rn;n > 1} be a sequence of real numbers such that rn → x,...
1. Let {rn;n > 1} be a sequence of real numbers such that rn → x, where r is real. For each n let yn = (1/n) E*j. Show that yn + x. HINT: (xj – a) Let e >0 and use the definition of convergence. Split the summation into two parts and show that each is < e for all sufficiently large n.
Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that...
Suppose that A is diagonalizable and all eigenvalues of A are
positive real numbers. Prove that det (A) > 0.
(1 point) Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that det(A) > 0. Proof: , where the diagonal entries of the diagonal matrix D are Because A is diagonalizable, there is an invertible matrix P such that eigenvalues 11, 12,...,n of A. Since = det(A), and 11 > 0,..., n > 0,...
(6) Let a be a positive real number. Note that for all r, y R there...
(6) Let a be a positive real number. Note that for all r, y R there exists a unique k E Z and a unique 0 Sr <a so that Denote (0. a), the half open interval, by Ra and define the following "addi- tion" on Rg. where r yr + ka and r e lo,a) (a) Show that (Ra. +a) is a group (b) Show that (Ri-+i ) İs isomorphic to (R, , +a) for any" > O. (Therefore,...
2. Let a be a positive real number, let r be a real number satisfying r >1, let N be an integer greater than one, and let tR -R be the integrable simple function defined such that tr,N(r) = 0 whenver x < a or z > ar*, tr,N(a) = a-2 and tr,N(z) = (ar)-2 whenever arj-ıく < ar] for some integer j satisfying 1 < j < N. Determine the value of JR trN(x) dz.
Real Analysis question, give clear writing please
Let h(x) be the function on (0, 1) defined by ſi x <1 h(x) = 2 X=1 (a) For any P, what is the value of L(f,P)? (b) Can you find a P such that U(f,P) is within 1/10 of L(f,P)? (c) Show that h is integrable.
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
1. Let p be a positive real number with 0 < p < 1, and let ni, N2, N3 be positive integers. Sup- pose that Xı has a Bin(ni,p) distribution, X2 has a Bin(n2, p) distribution, and X3 has a Bin(n3, p) distribution. Show that the random variable Z = X1 + X2 + X3 also has a binomial distribution, and find the parameters of that distribution.
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we would like to show that for all 0 SjSk-, the function satisfies the advancement operator equation (A -r)f0 (a) Show that this is true whenever J-0. You can use the fact that f(n) = crn satisfies (A-r)f = 0. (b) Suppose fm n) satisfies the equation when m s k-2 for every choice of c. Show that )...
Let α and β be real numbers with 0 < α < βく2m and let h : [α, β] → R>o be a continuous function that is always positive. Define Rh,a to be the region of the (x,y)-plane bounded by the following curves specified in polar coordinates: r-h(0), r-2h(0), θ α, and θ:# β. 3. (a) Show that (b) (c) depends only on β-α, not on the function h. Evaluate the above integral in the case where α = π/4...
Please do 10 & 11
Use Intermediate Value Theorem lial p(x) = x4 +7x = 9 has two real root. 8. df Open with Google Docs Then use your calculator to find the ro 9 Let f(z)2with € [0, 00). Find a positive mumber e and two sequences {xn} and {yn} such that lim-(nn) = 0 but |f(xn)- f(Yn)| 2 e. Then conclude that f(x) = x2 is not uniformly continuous on [0, ao) [0, oo). Show that f is...
1. Let {rn;n > 1} be a sequence of real numbers such that rn → x, where r is real. For each n let yn = (1/n) E*j. Show that yn + x. HINT: (xj – a) Let e >0 and use the definition of convergence. Split the summation into two parts and show that each is < e for all sufficiently large n.
Suppose that A is diagonalizable and all eigenvalues of A are
positive real numbers. Prove that det (A) > 0.
(1 point) Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that det(A) > 0. Proof: , where the diagonal entries of the diagonal matrix D are Because A is diagonalizable, there is an invertible matrix P such that eigenvalues 11, 12,...,n of A. Since = det(A), and 11 > 0,..., n > 0,...
(6) Let a be a positive real number. Note that for all r, y R there exists a unique k E Z and a unique 0 Sr <a so that Denote (0. a), the half open interval, by Ra and define the following "addi- tion" on Rg. where r yr + ka and r e lo,a) (a) Show that (Ra. +a) is a group (b) Show that (Ri-+i ) İs isomorphic to (R, , +a) for any" > O. (Therefore,...
Most questions answered within 3 hours.
-
Write a program to solve the Josephus problem, with the following
modification:
Sample Input:
./a.out n...
asked 2 hours ago -
At the start of a CD it is spinning at a rate of 525 rpm
(revolutions...
asked 2 hours ago -
4. Without doing any calculations, predict whether the observed
∆T would increase, decrease or remain the...
asked 4 hours ago -
Based on the range, which of the following sets of scores has
the greatest variability? 3,...
asked 5 hours ago -
Ripples in a pond travel at a velocity of 3 m/s with one peak
passing a...
asked 5 hours ago -
A man stands on the roof of a building of height 13.0 mm and
throws a...
asked 5 hours ago -
The extent to which assets are financed by borrowed funds and
other liabilities is indicated by:...
asked 6 hours ago -
Explain in detail
Germany is the fifth largest economy
explain what goods and services Germany specializes...
asked 6 hours ago -
The density of platinum is 21.45 g/mL. If a cube of platinum
with a mass of...
asked 6 hours ago -
Accounts Receivable
Sales
A/R Posting
Extended Sales Invoice
Packing Slip
Compare invoice to packing slip 2...
asked 6 hours ago -
Michaella, age 23, is a full-time law student and is claimed by
her parents as a...
asked 6 hours ago -
Why are polymers not typically casted into products?
asked 6 hours ago