Challenge. Establish the Cauchy-Schwartz inequality: For real numbers we have (a + az + ..+ a) (b+ b3 + .+ b) > (a1b1 + azb2 + .. + anbn)? with equality only if there is a constant k so that a; = kb; for each i.

Q: Which of the following ordered pairs satisfy the inequality 3x+2y= а. (0,0) .Ь. (5,1) с. (0,2.5) •…

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Q: b) Prove that + ≥ 2, for any nonzero real numbers a and b.

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Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: Find the maximum value of a, x, +a,x, + .+ax to the condition that x +x, +. + x =1 for given…

A: We need to find the maximum value of a1x1+a2x2+a3x3+...+anxn to the condition that…

Q: Find the set of real values of x for which a) > 3 by/2x- 3/ 0 13 Solve the inequality:x(x² – 6) >…

A: It is given that

Q: 8z + 7 < 3z – 4

A: Given: 8z+7&lt;3z-4

Q: 27) (x- 1)(x + 1) s0 A) {1} B) [-1, 1] C) (-1, 1) D) (-, -1]U[1, 0)

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: Ifx and y are positive real numbers, use the direct method to prove the following inequality: Vxy s*…

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Q: Find all the real numbers x which satisfy the inequality 1 7— 2х (2л — 7)2 and carefully sketch the…

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Q: The set of all solutions of the inequality 2|2x + 2] > 12 is

A: Given inequality  22x+2≥12 the above equation can be written as  2(2x+2)≥12 and 2(2x+2)≤-12…

Q: Write [4,7) using inequality notation. The inequality is (Type an inequality using x as the…

A: let x be a variable

Q: Assume the following three statements are true. p: For all real numbers x and y, if xy is…

A: We are given that statements p,  q and r are true. We need to prove that 2a-1 or a2+3 is…

Q: Let x and y be real numbers. Disprove: If |x| < |y| then |x+1|< |y+1]. Let x, y, and z be real…

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Q: 2. Definition. Let r be a non-negative positive real numbel A square root of r is the Iinique…

A: Note: Square of any real number must be non-negative and addition or subtraction of any two real…

Q: Give an example of numbers a and b such that |a + b| &lt; |a|+|b|.

A: To give an example of numbers a and b such that

Q: 2. Prove the statement: The sum of the squares of any two consecutive integers is odd.

A: I have assumed that n be any integer. Then i have found the sum of square of two consecutive…

Q: Does the Transitive Property of Inequality hold true for four real numbers a, b, c, and d? That is,…

A: Given: a,b,c,d b are four real numbers. Here, a&lt;b, b&lt;c &amp; c&lt;d

Q: Prove the inequality √1+x≤1+x2 for x&gt;1.

A: Consider the function. Find its derivative.

Q: For each nonnegative integer n, let Un = (n, -n]. Find U3

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Q: .A. Find the dmain of the following Fune tions :- 1. FOx)= V4-12X %3D

A: Given: F(x)=4-12x

Q: um value of -+ b + c c + a + a+b

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Q: Evaluate |⊂(R)| if R={n: n is a factor of 500}

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