Let r, y EN such that y # 0, then y+r#0.
Q: If u=f(x2+2yz,y2+2zx).Prove that
A: Given: u=fx2+2yz, y2+2zx Let u=fv, w where v=x2+2yz and w= y2+2zx. Now prove…
Q: Show that the subset of R2 given by {(x, y) E R² : xy 1, x > 0} is closed.
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Q: Let z=x+iy ∈ C where x∈R\{1}, y∈R, and |z|=1. If w = (z+1)/(z-1), then show that Im(w) = y/(x-1).
A: Use the following formulae, to obtain the required result. Real part of a+ib=aImaginary part of…
Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.
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Q: let H = {n² |n E z*}, determine whether it is closed under
A: Given : H={n2|n∈Z+} To Check: H is closed under binary addition or not
Q: Give the condition which ensure that Je-| < 1 where z E C.
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Q: let H = {n² |n e Z*}, determine whether it is closed under
A: Here, we have H=n2| n∈ℤ+. To show the set is closed under binary multiplication. This means we have…
Q: Show that the subset of R2 given by {(x, y) E R² : xy = 1, x > 0} is closed.
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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 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: Let x, y ∈ R such that x 0.001. Prove that |x · y| = |x| · |y|
A: Given: x, y∈ℝ, x<-0.001 and y>0.001 To prove: x·y=x·y
Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.
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Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express z x and zy in terms of fu , f y, and the…
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Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*
A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…
Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.
A: Given statement is false.
Q: Find the aven bounded by y=x and y =x+2
A: First draw the graph of the function and find the intersection point of the graph:
Q: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D
A: from above distribution is binomial f(x)θ=θx(1-θ)1-x ;0<x<1 E(x)= nθvar(x)=nθ(1-θ)…
Q: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…
A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…
Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at
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Q: Find the of im < Re z< £ un der w-
A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…
Q: Let f(x, y, z) = x²y°z – xyz², and compute: (a)
A: In this question we will use basic of vector calculus i.e gradient of any function and curl of…
Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…
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Q: if x, y>o such that x Sy then Vã svy Prove by direct method
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Q: According to boolean algebra x.(1 + y) =?
A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c (ii) Identity law :…
Q: ; Let x, y ER" be given. (a) lf ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…
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Q: Let X = R and Y = {(0, a, 0), a EE R} %3D %3D and V = {(b,0, b), be R} %3D Then X = Y e V %3D O True…
A: FALSE
Q: How to solve this?
A: We are given that x + y + z = 5 where x, y, z ∈ R. Now, we need to prove that x2 + y2 + z2 ≥ 5/3.…
Q: If X ∼ N (μX , σ2X ) and Y ∼ N (μY , σ2Y ) are independent, then prove X + Y ∼ N (μX + μY , σ2X +…
A: X~Nμx,σx2 and Y~Nμy,σy2 are independent. Here, X~Nμx,σx2. In this context, it is known that the…
Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.
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Q: Let E = XE[0, + 0) } then Sup E Маx E- %3D %3D x+ O True False
A: In this problem we have to determine Sup E and Max E, and check Sup E =Max E is true or false.
Q: Let f(z, y, z) = z2 +y? + z²,z = /utv, y = /u – v, and z= uv, Find in terms of u and v.
A: we have to partial derivative with respect to u by using chain rule
Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.
A: Solution:- The given question is Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…
Q: Y is neither on the interior, nor the exte Y lies in the interior or in the exterior of Y lies on…
A: In this question we will use basic of algebra. We will use basic concept of interior angle and…
Q: Let F I2). Evaluate JJaw as z² + y? 0
A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…
Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду
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Q: Prove that H(x, y) = (x, –y) provides a conjugacy between 1 X' = 1 X and Y' Y. 1 1 1 1
A: We are Given that : H(x,y)=(x,-y) X'=11-11X , Y'=1-111Y The Matrix H is corresponding to the…
Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).
A: X~Gammar,λ fx=λrΓre-λxxr-1, x>0, r>0, λ>0 Y~Gammas,λ fy=λsΓse-λyys-1, y>0,…
Q: Let F(x, y, 2) = (z, 1, y). a. Find divF and curlF.
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Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?
A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B
Q: prove with a table if x → y then xor y xor y = y
A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…
Q: 1. Let 1, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…
A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…
Q: at x and y are orthogonal
A: Given: x and y in ℝn, x+y=x-y To show: x and y are orthogonal in ℝn if and only if x + y = x − y
Q: Show for all x, y in R |x+ys]xl + ]y!
A: consider left hand side and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y
Q: Theorem:For all Xiyiz,w EN i) X<y ^ z sw =)x+Z <ytw ii) xsy ^ zw =) x+Z< y tw )x<う tsw 1 Esw うメ+ と x…
A: Solution: We know that for x,y∈ℕ If x<y then ∃k∈ℤ+,k>0 such that x+k=y If x≤y then ∃k∈ℤ+,…
Q: If X ∼ N (μX , σ2X) and Y ∼ N (μY , σ2Y ) are independent, then prove
A: X~Nμx,σ2x and Y~Nμy,σ2y are independant
Q: -x+y<y. 2 If x < y, prove that x <
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Q: Prove that if w = f(x,y,z), x=r-s, y=s-t, and z =t-r then ôw ôw ôw + âr' as = 0. ôt
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Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy
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