(-1)" :n Determine if A is bounded above, bounded 2. Let A = n below, or both. If it is bounded above (below) find the supremum (infimum). Justify all your conclusions.

Q: If x, y and z are three real numbers such that x+ y+ z= 4 and x + y + z = 6, then show that each of…

A: Introduction :

Q: Let A be a nonempty subset of positive integers and B = {n + v5 : n E A}. Show that B has a least…

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Q: Let I be a closed interval of the form [a, b], where a and b are real numbers and a ≤ b. We define…

A: Given that: Let I be a closed interval of the form [a, b], where a and b are real numbers and a ≤ b.…

Q: 4 State whether the following functions are injective and/or surjective. Let R* denote the…

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Q: Consider the interval. (2,6) Rewrite the interval using plus/minus notation. X ± 6 x Determine…

A: Given interval is (2,6)Lower confidence level=2Upper confidence level=6

Q: Srample: Let X~N(20,16) then find the prob that X lies within (1.5)

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Q: Let k be a positive integer. How many distinct functions are of the form g : [1..k] → [1..2k] such…

A: A function is defined when each value in the domain has exactly one value in the range. A…

Q: (B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a…

A: For (f) ,We use a theorem that "if n∈ℤ and n≠0 then n2>0.

Q: (a) Find the supremum of the set S:= 4 13 40 13 9 27 81.. }, if the supremum exists. Justify your…

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Q: Given f(x) = v3x + 5, f:R → R where R is the set of real numbers. а) Find the domain and range of…

A: We will find out all the required values.

Q: Describe in Roster form. (Don't put any spaces on your answers. Enclosed your answers in {).) {x…

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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: (1 – x²,x 1 in x= 0 1,x = 1

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Q: (1) + 1 2n :n EN

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Q: Exercise 6. Let R be a transitive relation. Let aR"b mean that there is a sequence of related…

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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.…

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Q: Write the formula of partial derivation with respect to x?

A: Partial derivatives  Let  f(x,y) is a function given , in which f(x,y) partially depends on x and y,…

Q: (2 points) Prove Prove that for all f: X Y and A, B C X, if f is one-to-one, then 4. f(A)n f(B) ≤…

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Q: * Given : the constants C,D; the functions F1 (1eof argum G/2; the predicates P/1, R12,Q13- Which of…

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Q: HW Hw2Find average te g change of fex) behween X = - frx) = and X=4 -x' -x²4 3x2 Ans 9 TryHW Gvaph…

A: Average rate of change of a function f(x) on the interval [a,b] is f(b)-f(a)b-a

Q: (Q4) Prove that if f : R → R is continuous function, and (n;)ien is a sequence of non-zero natural…

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Q: Let f(x) = |x − 2| − 1. i) Make a table of ordered pairs for f(x), for all integers x with −3 ≤ x…

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Q: 10) What is the domain of f(x)= vx + 5? A) {x|x 2 -5} B) {x|x 2 0} C) {x\x> -5} D) {x|xs -5}

A: Domain is set of collection of x for which f is defined

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: Let fx) = 3-402-11x. Use a sign analysis to find a) on which intervals is f concave up ? concave…

A: We need some basic definition here like concave up, conacave down, inflection points. So let's…

Q: Find, with a complete proof of all claims, the supremum, infimum, maximum, and minimum (if they…

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Q: de Ja V(z- a)(b – x) ‚a < b

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Q: k + 15k + 44

A: Let Uk=1k2+15k+44 Sequence Uk=144,160,178,198⋯⋯ Here, the sequence is continuously decreasing.…

Q: 0. Show where the fonction continuous ? is -4 1/2

A: The given function is,f(x,y,z)=x+y+z-4x-12

Q: Find: ii) P (X₂ ≤ 1X₂ ≤). f(x₁,x₂) = {1x1x² 0≤x≤1, 0≤ x₂ ≤ 1 elsewhere

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Q: Define local maxima with a figure in your own words. Give small ans

A: Local maxima : Local maxima would be the point in the particular interval for which the values of…

Q: Ax - B xS-1. 5) Given a function h(x) = {2x² +3Ax+B, -11 a) Given that h(x) is continuous for any…

A: As per bartleby guidelines, for more than one question asked only one is  to be answered, kindly…

Q: If |Z| ≤ 1 and w) ≤ 1, then show that |zw|2s (1z|-|w|)² + (arg z - arg w)²2.

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