my question is 11.11 in picture, another is hint .please use （1）in the hint, you should use “contruction by induction” 10.7 : Let S be a bounded nonempty subset of R such that sup S is not in S. Prove there is a sequence (sn) of points in S such that lim sn = supS. 11.11 Let t = sup S. There are several ways to prove the result. (1)Provide an inductive definition where Sk≥ max{sk-1,t - } forall k.k 11.11 Let S be a bounded set. Prove there is an increasing sequence (sn) ofpoints in S such that lim sn = sup S. Compare Exercise 10.7. Note:If sup S is in S, it's sufficient to define snsup S for all n.=

Answered: Image /qna-images/answer/367201ae-eb0f-4250-ad71-da59817a4c0a.jpg

Let S be a bounded set. Prove there is an increasing sequence (sn) of points in S such that lim sn = sup S. Compare Exercise 10.7. Note: If sup S is in S, it's sufficient to define sn = sup S for all n.

Let S be a bounded set. Prove there is an increasing sequence (sn) of points in S such that lim sn = sup S. Compare Exercise 10.7. Note: If sup S is in S, it's sufficient to define sn = sup S for all n.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Find A/B [17 46 A = 21 5 L33 2 11] 12 13] [4 43 B = = 3 L2 11 35 14 14 16 17

Q: Linearly dependent ✓ 1. f(t) = t² + 20t and g(t) = t² - 20t Linearly dependent V Linearly…

Q: 3. If you're tired or bored then you sleep (T, B, S). Therefore if you're hungry (H) and you're…

A: This is a problem of Logic.

Q: Prove that every positive integer n can be written as the sum of distinct powers of 2. E.g. 1 = 2º,…

A: we will use strong induction theory to prove the statement. statement is- " Every positive…

Q: he answers are set out in the following Hasse diagram: (image) - Write by extension the relation T…

A: This is a question of Set and Relation.

Q: Compute Projs w given by W = [2 -1 -2] and S is defined by x = s [2 − 1 2] + t [−1 −13], s, tER.

Q: Suppose you graph the function r(0) = 4cos (20) on the interval [0,2π] in polar coordinates. How…

A: Any point in the polar coordinate system is represented using the ordered pair: r, θ. At the origin,…

Q: max-(₁-4)²(x₂ − 4)² #1,22 x₁ + x2 ≤ 4, x₁ + 3x2 ≤ 9

Q: possible, write iterated integrals in spherical coordinates for the following region in the orders…

A: We need to use relation between cartesian and spherical system x=ρ sinφ cosθ , y= ρ sinφ sinθ , z= ρ…

Q: '0 8 3 تر محمد (1 + x)5 dx

A: According to guideline we need to solve one question. Rest of the questions should be reposted.

Q: This is the initial tableau of a linear programming problem. Solve by the simplex method. X₁ X2 S₁…

Q: Compute a Riemann sum using the right and left endpoints (sums) to estimate the total sales of the…

A: From the given details we have to find the average of the left and right sum. Average total sum =…

Q: Problem 5. Prove that n! > 2" for n ≥ 4.

A: Mathematical Induction is a mathematical technique which is used to prove a statement is true for…

Q: Find an SVD of the indicated matrix.

A: Let A=34 To find singular value decomposition (SVD) of A. The singular value decomposition of a…

Q: Translate a triangle with coordinates A(2, 2), B(6, 2) and C(4, 4) with translation vector [4 7]…

A: The vector (4 7) is saying it goes 4 across and 7 up as they are both positive.

Q: #9) (modified) A farmer with 800 feet of fencing wants to enclose a rectangular area and then divide…

Q: ← Minimize w=2y₁ + y2 +4Y3 subject to: with Y₁ + y2 +Y3 2 10 3y₁ + y2 248 Y₁ 20, Y₂20, Y3 20. The…

Q: For the given function, (a) find the slope of the tangent line to the graph at the given point; b)…

Q: Find the equation of the parabola by using three points (4,0), (2,8), and (6,0).

Q: wn = (-2)", Xn = 5(-1)^₂ Yn 1+ (-1)", = Zn = n cos (27)

Q: Solve the given system of differential equations by systematic elimination. (D+1)x+ (D-1)y = 5 6x +…

Q: Find the solution of each of the following problems. Identify the given, required, and the formula…

A: A paleontologist discovered an insect preserved inside a transparent amber. Amount of carbon-14 left…

Q: How much interest (to the nearest dollar) would be saved on the following loan if the condominium…

Q: Find all smooth curves that intersect the curves x² = y +Cx at the right angle.

Q: Find bases for the column space of A and the null space of AT for the given exercise. Verify that…

A: Basis: A set of vectors S is said to be a basis of a vector space V if S is linearly independent and…

Q: To purchase a car, Sarah took out a 60-month loan for $29,300 with a 7.6% annual interest…

Q: 23. Let w x₁ + iy₁ and 2 = x₂ + y₂. (a) Show that the distance WZ between the points w and z is |z −…

Q: Perform scaling on a triangle (1, 1), (8, 1) and (1, 9) with a scaling factor of 2 in both x…

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral 15…

Q: Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no…

Q: Question content area top Part 1 A student takes out a loan of $1,900 at the beginning of each…

A: Given Data: Student take a loan of $ 1900 at the beginning of each semester, for 13 semesters.…

Q: Find the 2 x 2 matrix that has as a 3-eigenvector and ר חר as a -1-eigenvector.

Q: A rectangle has a width (W) that is ten centimeters less than three-eighths its length (L) and a…

Q: 3. Let ABC be a triangle with D the midpoint of AB and E a point on AC so that DE is parallel to BC.…

Q: A detective is called to the scene of a crime where a dead body has just been found. She arrives on…

A: Solution: Given: The temperature of dead body TB1 = 80° F = 26.67° CThe room temperature TR = 68°F =…

Q: In the following Venn diagram, U is the set of students in a class, A is the set of students who…

A: Given: U=The set of students in the class A=The set of students who play soccer B=The set of…

Q: Suppose f: X→Y, and A, B CY. Prove that (a) f-¹(AUB) = ƒ−¹(A) U ƒ−¹(B). (b) f-¹(ANB) = f¯¹(A) n…

Q: Given the following graph of f (x) which starts at x = -T. Find the Fourier series of the function…

Q: This question concerns the linear system of differential equations dx dt dy dt = kx + (k² + k)y = x…

A: Given system of equations dxdt=kx+k2+ky…

Q: Find (3x + 2y)dA where R is the parallelogram with vertices (0,0), (4,5), (-3,1), and (1,6). Use the…

Q: e) A manufacturer produces three products: Product A, Product B and Product C. To be able to produce…

A: We can write the system of linear equations in the matrix form as Ax=b, where A is an m×n…

Q: IF AN ITEM IS VALID (V), THEN SHOW THAT IT IS VIA PROOF OF VALIDITY (S); BUT IF IT IS NOT VALID.…

Q: of

Q: Assume that the annual rate of inflation will average 3.8% over the next 10 years. a) Write an…

Q: (a) Consider the following phase line, where c is a positive constant. y=c y=0 i. Write down a…

A: The given phase diagram is: Here c is a positive constant. To Do: (i) Write the differential…

Q: Part F Find the times (to the nearest hundredth of a second) that the weight is halfway to its…

Q: Medical researchers developed a test that determines whether a person has a particular disease. The…

Q: (a) Consider the following phase line, where c is a positive constant. y=c y=0 i. Write down a…

A: Given: A phase line (i) We have to write a differential equation that represents this phase line.…

Q: dy dt = x + ky where k is a (real) parameter. (a) Write the system in matrix form d = AY. (b) Write…

A: This is a problem of stability analysis.

Q: Consider the phase portrait shown below for a system of the form dy dt = f(x, y), g(x, y), where f,…

A: As per the question we are given the phase potrait of the dynamic system : dx/dt = f(x,y) , dy/dt…

Question

my question is 11.11 in picture, another is hint .

please use （1）in the hint, you should use “contruction by induction”

10.7 : Let S be a bounded nonempty subset of R such that sup S is not in S. Prove there is a sequence (sn) of points in S such that lim sn = supS.