The domain of the functi f (x, y, z) = In(3.xy – 6) {(x, y, z) e R³ : xy < 2 {(x, y, z) E R³ : xy > 20 {(x, y) € R² : xy < 2 o {(x, y) e R² : xy > 2

Q: Let F(x, y) = x2 + x² + y2J- (a) Show that F. dr +| F. dr if C and C2 are the semicircular paths…

A: The function given to us is  F(x,y)=yx2+y2i-xx2+y2j

Q: The figure below shows the expression for the x-centroid of line L. Suppose length L is 10 cm and…

A: Suppose L is the length of the line. Then, the x-coordinate of the centroid of the line is…

Q: ind the maximum and minimum values of the function f(x, y, z) = ax + by + cz, where a, b, c are…

A: In the given question, maximum and minimum values of the function f(x, y, z) = ax + by + cz, where…

Q: Find the linearization L(x, y, z) of the function f(x, y, z) at the point. Then find an upper bound…

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Q: Cives とz f(xy)= J36-9メ-す i) Find domajn and Ram ge Foy the fuclien

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Q: X= R² and T = { $₁,x} V {₂\x>0} where U₁ = {(x, y) | x² + y ² < 2² } Prove (XT) is Topology

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Q: z=x+iy, consider the entire function f(z)=u(x,y) + iv(x,y) where u(x,y)=3x2y+2x2-y3-2y2. Prove that…

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Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: De'Morgan Theorem to prove that: (x.y'+x'.y)' = x.y+x’.y' %3D wwww

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Q: Compute the discriminant D(x, y) of the function. f(x, y) = x + y* - 6x – 2y² + 5 (Express numbers…

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Q: Integrate the function f(x, y, z) = 0.7(x2 + y2 + z2 ) over the unit sphere S ={(x,y, z) | x2 +y2+z2…

A: Given:  fx,y,z=0.7x2+y2+z2 s=x,y,zx2+y2+z2≤1 M=106 points

Q: ¸(1+ h)² −1 lim h→0 h using the squeeze Theor

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Q: Prove that af +y. -yof=nf (x, y). əx (Hint: Differentiate both sides of the definition of a…

A: Given  a) x∂f∂x+y∂f∂y=nf(x,y)b) x2∂2f∂x2+2xy∂2f∂x∂y+y2∂2f∂y2=n(n-1)f(x,y)

Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…

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Q: Find a formulaforvectorfield F= M(x,y)i+ N(x,y)j given the fact that for all points(x,y),Fpoints…

A: Any point, x,y in the two dimensional space can be defined by a position vector, v→=xi+yj .

Q: A necessary condition for the functional J defined by X2 J(Y) = | dx f(x, Y(x), Y'(x)) to have a…

A: The function J(y) is defined and a necessary condition for the functional J is defined…

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: Find the maximum and the minimum of the function f(x, y, z) = 2(x+y+z)- xyz on the set {(x, y,z)|x²+…

A: Let gx,y,z=x2+y2+z2. Differentiate the functions f(x,y,z) and g(x,y,z) partially with respect to x,…

Q: x+y if (x, y) # (0,0) (1 if (x,y) (0,0) Q.3 ( 3+3+4) (a) Prove that the function f(x, y) is not…

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Q: F(X)=JX F: [o,2]-> show i fis lipschit z funcla or not find k to

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Q: Find real differentiable functions s(y) and t(y), such that the complex function f(x + iy) = e"…

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Q: (z2 – 4)(z² – 3z – 10) (2² + 4z + 4)(z² – z (15) Find the singularities of the function f(z) =…

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Q: Find the number of zeros of f(z) = 2z* – z + 5z – 1 in the annulus 1 < |z| < 2. %3D

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Q: Suppose that (z) is entire and that the harmonic function u(x, y) = Re[fz)] has an upper bound uo;…

A: As requested following is the answer for question 12.

Q: What is the maximum of the function f(x, y) 2xy+ 2x - 2x2 - y²? %3D O a. (x, y) = (1, 1) O b. (x, y)…

A: We use second partial derivative test to find critical point where value of f(x,y) is maximum

Q: Test the function def ined by f (x,y) = - x- 4y for its homogeneity. If it is homogeneous, give its…

A: Find your answer below

Q: The function f(x, y) = ¿e=y – In(y²)

A: It is partial derivative

Q: ind the maximum value of the function f(x,y,z) = x² + y² + z² on the plane x+y+z = 1.

A: The given function is; f(x,y,z) = x2+y2+z2

Q: z is a complex variable z=x+iyShow that f(z)=((z^2)+1)/((z^2)-3z+2) is continuous for all z outside…

A: The problem concerns the continuity of a rational function over an open set.

Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: X = R² and = = { $₁x} V { \\x>0} where U4 = {(x,y) | x² + y² <²} Prove (x, t) is Topology

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Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

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Q: (2) Use Green's theorem to calculate f. F - di for F(x, y) = (x2 + y, e") and C the boundary of the…

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Q: The real and imaginary parts of z=x+iy are Imz=x ERO Rez=x ERO Rez =y ERO Imz=y ERO

A: Consider the given complex number. z=x+iy Now, write the real number and the imaginary part of the…

Q: Find the maximum value of the function f(x,y,z) = plane x+y + z = 1. x² + y? + z² on the %3D

A: The solution is given below in the next step:

Q: Q2 A) for F= 2xi-3Y3+K %3D prove That div( curl È)=0

A: Given :          F→ = 2x i - 3y j + k   To prove that div(curl F→ ) = 0

Q: ✓(3) Prove Green's theorem for F = Y Z + x²y³j y (1,1) i (1,0)

A: Solution of the given problem is below...

Q: - Let f(z) = cosh z. (1) Find the image of S := {z = x+iye C: x < 0,0 < y < } under f.

A: Follow the steps.

Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

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Q: 2- Show that the function U(x,y)= 3x²y-y² + y is Harmonic and then find it's Harmonic conjugate V(x,…

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Q: 5z +3 Find the domian of not analyticity of f(z)=. sinh z -i a O (T + 2kx)i 2+(+2k7)i .c O (エ +…

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Q: Consider the function f(x, y) = 36x2 – 19y + 18xy over the unit square 0 <x < 1, 0 < y < 1. %3D -…

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Q: 5z+1 2. Prove that the function f : R – {2} → R – {5} defined by f (x) = is bijective. z-2

A: Consider the given information: The given function is, f:ℝ-{2}→ℝ-{5} f(x)=5x+1x-2 To show that f is…

Q: (b) Show that the function f(2) =u +iv, where S(2) = **(l+1) – y'(1-1) x² + y² = 0, z = 0 Satisfies…

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Q: f(r, y) = VI y (c) Prove that the function z-f(x.y) doesn't have any local maximum or minimum in D.…

A: Given : Multi variable function f(x, y)  To find : Need to show that function doesn't have local…

Q: Find curl F if F(x,y,z) = 7exy i-8 cosy j +5 sin²z k. curl F = -7xexy k curl F = -7xexy i curl F =…

A: In this question, we want to find the curl of given vector function.

Q: Y A B C Given: XC bisect YB at A; A is the midpoint of YB Prove: AXYA = ACBA

A: We have to prove that given Triangle are congurent.

Q: A. Compute for Coefficient of r Let x ΣΥ Ξ [x² = Y n= [x = [xy = £y = r= Analysis & Interpretation…

A: Solution-: Let, X=Weight (lbs) and Y=Chest size (cm) We have following data: X Y 5.64 29.5…

Q: 9: Find the Zero Cnd its た Aunction fに)、1にかi+Z+を。 Oroler

A: We know that, a function f(z)= (z-z0)n has zero at z0 of order n if f(z0)=0 at z0.

Q: d= uppose that z = f(x, y) is differentiable at the point (16, 8) with f,(16, 8) = 3 and f,(16, 8) =…

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