Question 4. Prove that L°[0, 1] C L°[0, 1). Hint: Hölder's inequality

Q: What is the global minimum of the function, x² 5 f(x) 3 + 2 on the interval [-2, 2] ? a) 2 b) 23 3…

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Q: Let A = the set of straight lines in the xy-plane. Let a L b mean “line a is parallel to line 6”.…

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Q: 12. For each n € N, define A, = [0, 1+] and B₁ = [0,1]. - =1 (a) Prove that U1A,, is an interval,…

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Q: What is the Brouwer fixed point theorem and how is it connected to the notion of retracts?

A: To Explain :  Brouwer's Theorem and how it is connected to the notion of the retracts.

Q: Prove the Cauchy-Schwarz Inequality, ∣u ∙ v∣ ≤ ∣ u∣∣  ∣ v ∣∣.

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Q: التاريخ 27 أمر موح let I = (a,b) be an open interval show that - for every positive sM(IDS.

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Q: ju the linear functiono from IR into proof that my ove Lipschitz, low is the triang le inequality…

A: It is given that In the proof that linear function from IR^n into IR^m are lipschitz

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: The value of the Wronskian of set of functions {x² - 3x +1, 2x² - 6x + 2} is O a. 13x O b. 7x? 2x? O…

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Q: Show that the interval [a,b] is complete

A: Given

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

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: (a) Let a, b e V and suppose that ||b+a|| = 0 and ||b – a|| = 0. What can be said about a, b? Prove…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is true about the function *) - as *-* ? A) B)(x)→0 from below OC) f(x) is undefined OD)x)→…

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Q: Let (x, eA) be a measurable space, £: X (-∞, w) and 9:* (-∞0, ∞o) are measurable. Prove that the…

A: Given that X,A is a measurable space. The objective is to prove that the sets  {x∈X:f(x)<g(x)},…

Q: يثبت The Cauchy-Schwarz inequality states that (f, g)| ≤ ||f||||g|| for every f, g ¤ H.

A: Using the property of inner product

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: If 4 p and q P крса are conjugale exponent a measure X a measure space, p р. f₁g:x [₁₂+] measurable…

A: Given P and q are conjugate exponent and f,g are measurable function and let p,q∈(1,∞)

Q: (b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact that ||ax + by |…

A: Given that, Euclidean metric d on Rn is defined as d(x,y) = || x - y || for x, y in Rn Part(a): Let…

Q: 1. Let a be a positive real number and n be a natural number. Define S = {x €R: x >0 and x" a?…

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

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Q: Show that in R with the usual topology, the only open sets connected by trajectories are the open…

A: Given that R with the usual topology  A collection of of subsets of R which can be expressed as a…

Q: 2. Let a € R be given. Define f: R" → R by f(x) = a¹x, x = R¹. Using the € - & definition, show that…

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Q: Let (X, CA) be a measurable space, f: X (-00, ws) and 1: X (-∞, ∞0) are measurable. Prove that the…

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Q: Prove that the infimum and the supremum of the interval (a,b) are a and b, respectively

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Q: Determine the maximum value of f(x)=-x²+2x²+2 on -2 ≤x≤ 3. a) 3.185 b) -7 Od 2 d) 18 2

A: To find the maximum value of the function.

Q: Prove that interval [0,1] is uncountable.

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Q: 1- Find the set of lower bounds and the set of upper bounds of the following sets in R, if it…

A: Since you have posted multiple sunparts of a question so according to our guidelines we will solve…

Q: Prove the inequality |arctana−arctanb|≤|a−b|.

A: To prove the given inequality.

Q: Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

A: Consider the given inequality in the given interval. Use the graphical approach to prove the…

Q: How is the nullspace N(C) related to the spaces N(A) and N(B), if C = [ A/B] ?

A: Given: N(C) is a nullspace and C=ABTo find: The relation between N(C),NA,NB matrix wise.

Q: Which characteristic/s implies(y) that a set S of real numbers is closed? S has no accumulation…

A: To choose correct option from given question.

Q: (2) Show that C(0, 1] C L'(0,1]. Compare |flsup and fl. Justify your answer. Generalize this to the…

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