5. (10 points) Prove that for all positive real numbers r and y, one has the inequality > 2 (u+ 112 < 4.

Q: Which of the following sets is not closed for the operation °, which is defined by the rule a°b = a…

A: The objective of this question is to determine which set of integers is not closed under the…

Q: Theorem 6 If (b+ f) > (c+r) und (d+g) > (e+ s), then the necessary und sufficient condition for Eq.…

A: (P+Q)2 = P2 +Q2 + 2PQ P2 +Q2 + 2PQ = (P+Q)2 P2 +Q2  = (P+Q)2 - 2PQ

Q: 13. Let U be the set of real numbers, A = {x |x is a solution of x - 1 = 0}, and B ={-1, 4}.…

A: Let's find.

Q: Question 4 > Solve the following quadratic inequality: x + x – 30 < 0 Write your answer in interval…

A: Solution

Q: n! Prove that the maximum value of when n. +n2 t+ nr =n n.! n.! na! ... is given by n, = na = = ny =

A: The expression n!n1!n2!...nr! will be number of different permutations of n objects with n1, n2...nr…

Q: Consider the set = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X Show that x₁ + x2 + x3 ≤ 2 is…

A: Here, in the question a set is given : X={x∈R4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4 ∈ {0, 1} } We…

Q: 1) @ê Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X3, X4 = {0, 1}}. Show…

A: Given: Set: X=x∈ℝ4 / 93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4∈0, 1To Show: b) ConvX is a…

Q: XA and x & f(x)}. Show Cim ƒ.) 38. Let a, b, c, and d be any real numbers such that a < b and c < d.…

A:

Q: Find all z belong to C sastifying the given equation or inequality J (b) |z5|+|z+1|≤|z2| -

A:

Q: Find all possible pairs of natural numbers that add up to 900, such that one is divisible by 14 and…

A:

Q: 1) (b) (c) Consider the set X = {x € R¹ / 93x1 +34x2 + 26x3 + 18x4 ≤ 131, x1, X2, X3, X4 € {0, 1}}.…

A: Given: Set, X=x∈ℝ4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4∈0, 1We need to show that the valid…

Q: 7) State the maximum and minimum values if they exist. P = 2x + 7y [4x-2y ≤8 {x≥1 [0sy 4

A: Given information P=2x+7y subject to,  4x-2y≤8          x≥1   0≤y≤4.

Q: Which of the following applies to the interval 0<x<4 for (x)/(x+1)<(x)/(x-4) if the inequality has…

A: Consider 0&lt;x&lt;4 and xx+1&lt;xx-4 Now,…

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: 15. Given g(x) = 2x+-x-29x2 +34x +24 a) use the upper bound to complete the interval [-6, ?] in…

A: Firstly we can find zeros and upper bound in which all real zeros lie.

Q: Since P+ Q, it follows that [(a1 + a3 + a5) – (a2 + a4)] [(B1 + B3 + B5) + A (82 + B4)]' | P+Q =…

A:

Q: mutually disjoint? Why or why not?

A:

Q: b) Prove that 3abc ≤ a³ + b³ + c³ for nonnegative a, b, c. (Hint: In the in- equality of part (a),…

A:

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: (a) Prove that the function f is well-defined; that is, the value f(q) of the function at a rational…

A: Given the notation , and using this defining the set . Then the function  defined as:.It is well…

Q: 4. Intro To Real Analysis

A: Step 1:Solution- Step 2: Step 3: Step 4:

Q: so there is no solution on that interval?

A:

Q: Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined as f: R ->…

A:

Q: 9. Using calculus to show minimum and maximum values taken by functions, find and prove(Create your…

A:

Q: + a3 + a5) – (@2 + đ4)I 4 [(a1 + a3 + as) – (a2 + a4)] [(B1 + B3 + B5) (a2 + a4) + A (B2 + Ba) (a1 +…

A:

Q: 20. Use forward reasoning to show that if x is a nonzero real number, then X + 1 > 2. [Hint: Start…

A:

Q: 9. the series diverges by the 2. Thus the series converges when r + 3| < 1, or - < a < -. At z = -…

A: