If xly, then show that ||x+ y|| = ||x- y|!.

Q: b. Prove that coth² x-1=csch?x

A: Sinh(x)= (e^x-e^-x)/2. Cosh(x)=(e^x+e^-x)/2

Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

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Q: 4. Show that if ki = (X; – X)/[Σ(X; – Χ)2], then (a) Σ ki = 0; = (b) Σk? = 1/[Σ(X - X)]; (c) Σk;(X;…

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Q: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

Q: 5. prove thatS" erf (x) dx =o CA

A: ddx(erf(x)) =2 e-x2π   I =∫-aa erf(x) dxI= erf(x) x -∫ ddxerf(x) x dxI = x erf(x) -2π∫ x e-x2 dx-x2…

Q: If A= then A" + nl is equal to 1.

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Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

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Q: of Voots of the equation. 2x+3X+5=0 is The muttiple is Ę 2. 3 Prove That The sum

A: Use the formula for the sum and product of the roots of a quadratic equation.

Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x\ ym – zn for m,n e Z 2)…

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Q: If xly then gcd(x,y) = y. إختر واحدا:

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Q: xy If z show that: x- y

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Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

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Q: If Z = eax + by F(ax - by); the value of %3D az is + a ду az

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Q: (3) Let X = n(u, 4) and Var(2x) = E(4 – 7x) find µ.

A: Given X is normal distribution with  mean =μVaraince σ2=4Standard deviation =4=2 If X has Variance…

Q: Let X ~ N(0, 1). For any € > 0, show that P(|X| > c) ≤ ²c - ??

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Indicate the method you would use to prove the two A's . If no method applies, enter "none". of

A: Given ,  Here ,  Two angles are equal and one side is equal .

Q: prove that erf (x) dx =o

A: To prove: ∫−aaerfxdx=0

Q: Prove that d (sec"x)= 1.

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Q: z equals 1 If 1, then וא

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Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: -2x -dx - Evaluate (1-x)' 8 А. х* + 6х- In(1-х)' + 1-х 8 -(1-x)* +C С. х? +6х+ In(1-х)' +- -(1–x)*…

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Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

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Q: -10 If AXT = B, then X= Let A = %3D 0 2

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Q: The characteristic of Z3[x] is 6. a) True b) False

A: Determine whether the given statement is true or false.

Q: If ADEF ARST, then we can conclude that ZR

A: Explanation of the solution is given below...

Q: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

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Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: If k> 0 such that k S x 8k dx = 7 then

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Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: 1. Do not use a theorem to find the ff. Z if yz? + z = 5xy – 1. %3D

A: In the multivariable function, if we have to find the partial derivative of one variable with…

Q: Fincd dy for y-sinner} er tot

A: Explanation of the solution is given below...

Q: 3. f(г, у) 3D In(х +y)

A: The differentiation of  ln x = 1x

Q: (a, 0) is not measurable.

A: In this question, we check the given set is measurable or not. here we use the condition of Lebesgue…

Q: az If x2 + xy + yz + z2 = 6, then- ду

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Q: If In(ax)dx = 2, then a = %3D 1

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Q: The characteristic of Zs[x]/ is 6. O None of the choices

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Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

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Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

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Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: By 2 Cas X the Same. way prove that

A: Prove that J-12x=2πx cosx

Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

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Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

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Q: Find a number 8 such that if |x – 2| < 8, then |4x – 8| < ɛ, 11) where ɛ %3D 0.01.

A: Ffind the delta