Consider E={-2+1/n} n=1 to infinity U (3,9) as a subset of R with the usual definition of < (less than) a

Q: If A = {x+|x-1| : xER), then which of ONE the following statements is TRUE? A. Set A has a supremum…

A: We use the definition of modulus function to solve this problem.

Q: If A = {x+|x-1| : xER), then which of ONE the following statements is TRUE?

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Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: Which of the following are true for a function of odd degree with a negative leading coefficient? a)…

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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: Suppose that f(x) is convex and continuous on an interval I. Show that dif(x1) + ·.+ A„f(xn) + Anf…

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Q: Prove that x² + ¹² +2111²2 = y 1112 where prime denotes differentiation w.r.t.s. 1 1+p¹² 4 p² o² + P

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Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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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: Juppose that the Mumber On ole det Bively by ogas for all nz2. Show that Oh= 2 +3( recu true for…

A: true

Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

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Q: -. For any integer m and any real number x, if x is not an integer, then [x]+[m- x] = m-1.

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Q: Find the lexact and then appeximate) value (s) of K that will make the given function continous over…

A: Finding the left and right limits at x=4:

Q: 2. Determine the domain and range of the functions below. a. f(x, y) = |*/v4| for any real numbers x…

A: Please post the multiple question separately. Here I answered 1st question as per our policy.

Q: Prove that there is an additive function T : R --&gt; R that is not linear.

A: Let T: V→W  be the linear transformation and we it is linear,…

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: Let X={X1, X2, X3, X4, X5) and A = 0.7

A: Given: To explain the correct option of the given statement as follows,

Q: A. If X~N(196,20), find x such that Pr(X < x) = 0.945.

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Q: Prove that x² +¸µ111² +21112 where prime denotes differentiation w.r.t.s. = 1 o² + 1+p¹² P

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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: a_ if f(z) is analytic function, show th 2 8²) | f (2)| = + | f (2)| ² 78 Dy12

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Q: Let A =[1 1        1 0] (in the giant brackets I just don't know how to do that on here) . Show that…

A: Given,A = 1110To show:An= fn+1fnfnfn-1

Q: Q1. Find the image of the set A= [-2 under function sin x.

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Q: Which of the following function is NOT Q, (n)? А. п —333п? nlgn С. п-1gn D. 219 n E. None Е.

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Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

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Q: Find the term independent of of in the expansi Ansion of √x 3 + 3 222 to

A: Given expression is x3+32x210. The aim is to find the term independent in the expansion of the above…

Q: f. Is the domain of f(x.y)= In (6x + 5y“) bounded or unbounded? O Unbounded O Bounded

A: the domain will be Unbounded because

Q: Find ||f||sup if - f(x) = x on (-1,1). -. f(x) = 0 {²-2² if x EQ, -x² if x #Q, for all x ER.

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Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: 4. Prove that the interval (0, 1) does not contain a smallest value x.

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Q: Let P(z) = z" +am-12"-1 + ... + a1z + ao be a polynomial of degree n 2 1 with a; # 0 for at %3D…

A: We will solve Q9 as mentioned. Given Pz=zn+an-1zn-1+…+a1z+a0 be a polynomial of degree n≥1 with ai≠0…