Show that if a; b R then (a) max{a; b} = 1/2 (a + b +

Question:

Show that if a; b ∈ R then
(a) max{a; b} = 1/2 (a + b + |a - b| and min{a; b} = 1/2 (a + b - |a - b|):
(b) min{a; b; c} = min{min{a; b}; c}:

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

See More Books

Question Posted: Apr 07, 2016 10:53 AM

See More Questions

(a) Show that if a > 0, then 1/a > 0 and 1/(1/a) = a. (b) Show that if a < b, then a < 1/2 (a + b) < b.
Show that if a > b, then b-1 > a -1, provided that a and b have the same sign. What happens if a > 0 and b < 0?
Show that if A , B, and C are square matrices, then det = (det A) (det B). A O C B
Multiple Choice Questions 1. Direct materials are not usually easily traced to a product. A) True B) False 2. Product costs can be classified as one of three types: direct materials, direct labor, or...
Solve the linear programming model formulated in Problem 41 for Island Publishing Company by using the computer. a. How much would it be worth to Island Publishing Company to obtain enough additional...
The equity section of Ahab SA at December 31 is as follows. Instructions From a review of the equity section, as chief accountant, write a memo to the president of the company answering the following...
Consider the periodic signal \[f(t)=\left\{\begin{array}{lr}\cos (t)+D, & -1 \leq t \leq 0 \\\sin \left(t^{6} ight) / t^{3}, & 0 \leq t\leq 2\end{array} ight.\] where \(D=\sin \left(2^{6} ight) /...
Use the transition matrix in Table 21.1 and software on the authors web site to calculate the transition matrix over 1.25 years.
3. Starting with the following AVL tree: 100 50 200 30 80 Perform the following operations cumulatively in the order given. For each operation draw: The tree after the operation but before any...
On January 1, 2020, Prasad SpA had the following equity accounts. Share CapitalOrdinary (25 par value, 48,000 shares issued and outstanding) .......................1,200,000 Share PremiumOrdinary...
Determine and sketch the set of pairs (x, y) in R R that satisfy: (a) |x| < |y|; (b) |x| + |y| < 1; (c) |xy| < 2; (d) |x| - |y| > 2:
If x; y; z R and x < z, show that x < y < z if and only if |x - y| + |y - z| = |x - z|. Interpret this geometrically.
Back Country Outfitters Inc., based in Nelson, British Columbia, assembles snowboards for the serious snowboarder. It buys the boards already cut to size and adds the various fittings required to...
In a small handloom mill there are four looms working continuously. Occasionally, the looms breakdown for which a repairman is called. On an average the service requirement is at 10-hour intervals...
Gather minimum five articles related to the Toyota scandal related to unexpected acceleration. The articles could be both from journals or newspaper article styles. Go to popular news web sites such...
A company annually uses 24,000 units of a raw material, which costs Rs 1.25 per unit. Placing each order costs Rs 22.5 and the carrying cost is 5.4 per cent of the average inventory. Find the...
Explain the concept of duality in the context of constrained optimization and its implications for understanding the interplay between objective functions and constraints in mathematical programming?
Ellen Goldberg, an equity analyst, has been tasked with valuing Intel Corp. (INTC) using the free cash to the firm methodology. Goldberg gathers the following information for INTC for the most recent...
In Exercise 29, we considered whether a linear model would be appropriate to describe the trend in the number of passengers departing from the Oakland (CA) airport each month since the start of 1997....
The first law of thermodynamics is sometimes whimsically stated as, You cant get something for nothing, and the second law as, You cant even break even. Explain how these statements could be...
The figure shows a horizontal line y = c intersecting the curve y = 8x - 27x3. Find the number c such that the areas of the shaded regions are equal. y= 8x-27x3
(a) Show that the volume of a segment of height h of a sphere of radius r is V = 1/3 Ïh2 (3r - h) h
Water in an open bowl evaporates at a rate proportional to the area of the surface of the water. (This means that the rate of decrease of the volume is proportional to the area of the surface.) Show...
a) Give examples of low, medium and high strain rate test types. [4 marks] b) A plot of log (stress) against log (strain rate) provides a straight line relationship. Based on this, provide an...
3- Let the density of the pyramid material be p = 2000 kg/m. Determine the average normal stress at a cross section located at x measured from the apex. Express the stress as a function of x. Assume...
You are designing a wing with no aerodynamic twist based on the airfoil camber given by: N C 3.1 (H-H) = 0.1 The wing will have an aspect ratio of 10, a taper ratio of 0.8, and a constant geometric...

Show that if a; b R then (a) max{a; b} = 1/2 (a + b +

Question:

Step by Step Answer:

a If a b then maxa b b 12 a b ...View the full answer

Introduction to Real Analysis

Students also viewed these Calculus questions