Prove that if a, bER and a < b, then |(a, b)| = |[a, b)| = |(a,b]| = b – a. %3D %3D %3D

Q: Let ū = (-1,2,4) and ū = (-3,5, 2). Compute the following: (a) ū+ū (b) .공 (c) ||해 (d) ũ - 7 (this is…

A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

Q: 10 Sx³ex¹⁰dx= (Type an exact answer.)

A: Given integral is as follows

Q: Find each quantity if v=3i-5j+2k and w =2i + 3j - 2k. ||v||+||w||

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Q: QB3% Let C=2+3i u= ( 1²/13 + 2/2 ²,0, 1/3-2²) v = ( 3²/3 + 4/1/², 1/3-2, 0) Calculate a) 2-3i b)…

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Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

Q: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully…

A: This is a problem of point-set topology.

Q: 2) Let R' real numbers, define = x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is…

A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

Q: If X~ Unif (o,1) and YeaX+b~Unt (-I,i), ? then what are a,b a = ? b=? the values of a and b in this…

A: Probability distribution

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are %3D %3D two sets. find R = {(x, y): x E X and y E Y…

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Q: Re(z,€,) = Re(*,)R (z,) O True O False

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Q: c) Find u (v x w) if u = [0,0, p], v = [0, q, 0] and w = [r,0,0]. %3D

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Q: |u| = |v| is equivalent to u =. or u =

A: Given that u=v Recall that the absolute value sign gives the positive output for both positive and…

Q: ..+n = n(n +1) 2. prove that 1+2 +3+ %3D for n=L,2, 3

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Q: Property IV : Two independent variables are uncorrelated. independent variables then r (X,Y) = 0.…

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Q: Let A = {1,2,3} and let R= {(1,1), (2, 2), (3, 3), (1, 2), (2, 1), (3, 2)} C A x A. In each case,…

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Q: Suppose AE R, v#0, and (A- A)v#0. Use the fact that A is symmetric show that it is impossible to…

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Q: U= 2i-35 j V = 59 +3

A: Given: u=2i−3jv=5i+3j

Q: Set f(a,b) = (1+ a + b) + (2 + 2a + b)x + (1 + a + 26)r² and F = {f(a, b) : a,b e R} a subset of…

A: Given that fa,b=1+a+b+2+2a+bx+1+a+2bx2 and F=fa,b : a,b∈ℝ is a subset of ℝ2x. The objective is to…

Q: u = [2, 6, –5] and v= [-3,–1,6] %3D A · A + (A + ng-) · (A x n)

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Q: Let y = Ա 4 + DIS 5 Ա and u = x³ = x³ - 2x.

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Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: Find the distance between m [-2, 3, 2,0,3, – 13, –5] and n = [4, –1,1, –5, 0, 11, –3].

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Q: = [4, 3, 0] v = [-2,0, –3] u = u x v = Ex: 5 Ex: 5 Ex: 5

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Q: Let R = (6, 5). Calculate the length of OR. ||OR||

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Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

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Q: Find all values of z such that z5 =1 - i.

A: Given: z5=1-i, To find: All values of z.