(a) Explanation Given information: The function f ( x ) is f ( x ) = ( a 1 x + b 1 ) 2 + ( a 2 x + b 2 ) 2 + ⋅ ⋅ ⋅ + ( a n x + b n ) 2 . Calculation: Provide the function as shown below: f ( x ) = ( a 1 x + b 1 ) 2 + ( a 2 x + b 2 ) 2 + ⋅ ⋅ ⋅ + ( a n x + b n ) 2 (1) The function f ( x ) = ( a 1 x + b 1 ) 2 is a quadratic function of the form ( a 1 x ) 2 + ( b 1 ) 2 + 2 ( a 1 x ( b 1 ) ) with coefficient of a = ∑ a 1 2 , b = ∑ a 1 b 1 , c = ∑ b 1 2 . Expand the equation (1). f ( x ) = ( a 1 x + b 1 ) 2 + ( a 2 x + b 2 ) 2 + ⋅ ⋅ ⋅ + ( a n x + b n ) 2 = ( a 1 2 x 2 + 2 a 1 b 1 x + b 1 2 ) + ... + ( a n 2 x 2 + 2 a n b n x + b n 2 ) = ( a 1 2 + a 2 2 + (b) To determine Prove that the equality holds in the Cauchy-Schwarz inequality provided there exists a real number x which makes a i x equal b i for each value i from 1 to n .

University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)

3rd Edition

ISBN: 9780321999610

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

See similar textbooks

Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 4, Problem 34AAE

(a)

To determine

Deduce the Cauchy-Schwarz inequality.

(b)

To determine

Prove that the equality holds in the Cauchy-Schwarz inequality provided there exists a real number x which makes aix equal bi for each value i from 1 to n.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 33AAE

Chapter 4, Problem 35AAE

Students have asked these similar questions

Hale / test the Series 1.12 7√2 2n by ratio best 2-12- nz by vico tio test en - プ n2 rook 31() by mood fest 4- E (^)" by root test Inn 5-E 3' b. E n n³ 2n by ratio test ٤ by Comera beon Test (n+2)!

Evaluate the double integral ' √ √ (−2xy² + 3ry) dA R where R = {(x,y)| 1 ≤ x ≤ 3, 2 ≤ y ≤ 4} Double Integral Plot of integrand and Region R N 120 100 80- 60- 40 20 -20 -40 2 T 3 4 5123456 This plot is an example of the function over region R. The region and function identified in your problem will be slightly different. Answer = Round your answer to four decimal places.

Find Te²+ dydz 0 Write your answer in exact form.

Chapter 4 Solutions

University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)

Ch. 4.1 - In Exercises 16, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 3E Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.