DNE.) +2+ f defined on |-1,3] maximum (x, y) = minimum (x, y) = Need Helo?

Q: If (2) = u(x, y) + iv(x, y) is analytic in a domain D, then using first principles- that %3D dv du…

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Q: Find the absolute maximum and minimum values of f(x, y) = x² - 3x + y2 - 3y + 5 on the triangle…

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Q: v dA , R is bounded by r= 2– cose R

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Q: The absolute minimum of f (x, y) = x² +y² – 2y on the semicircle region D= {(r,y) | y> 0, x² + y? <…

A: Given function is fx,y=x2+y2−2y and D=x,y|y≥0,x2+y2≤4. We have to find the absolute minimum of fx,y…

Q: ∫∫R dydx; R={(x,y)l(0≤x≤1),[√(x)≤y≤√(4-3x)]}; R=limits

A: We will solve the following

Q: Find the absolute maximum and minimum values of f(r; y) = r +y- y² – 3 on the upper half unit disc…

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Q: Find fr and fy- pry S(27, y) = /" 2e" dt %3D f.(r, y) = | f„(x, y) = | %3D

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Q: Find the absolute maximum and minimum values of f(r;y) = ² + 2y – y² on the upper half unit disc %3D…

A: Note:- In given problem, unit disk is mentioned then y will be positive that is, y≥0. But in D you…

Q: . Find a function ó(r, y) that is harmonic in the washer {z E C: 2< |z-1-i|<3} and satis the…

A: Let us find   phi value in terms of x and y....

Q: Among all rectangular boxes defined by the inequalities 0 ≤x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1, find the one…

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Q: 5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18). R h…

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Q: Consider the function f(x, y) = ax – 2y + 1 where a is a positive number. S SR ax 2y + 1 dA = 45,…

A: A double integral involves the integral with respect to the product of any of two variables in x,y,…

Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is  f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

Q: over the open surface S given by the upper part (only) of the intersection of ti of the function z =…

A: Introduction: Stokes Theorem (also known as Generalized Stokes Theorem) is a statement about the…

Q: Use Stoke's Theorem to evaluate · F · dĩ where F = (xz, xy, 3xz) where C is the boundary of the…

A: Using the Stoke's theorem we have to evaluate  ∮F.→dr→ where F→=xz,xy,3xz=xzi+xyj+3xzk such that the…

Q: Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or…

A: If f(x,y) is function of two variables then the points which satisfyfx=0fy=0 are known as a…

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

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Q: Given that F = (2x + y2)i + (3y – 4x)j. Verify Green's theorem for F.dr around the triangle formed…

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Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y.z) = In (3z° - 4x- 5y- 4) 1…

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Q: The value of the line integral | F(r).dr when C F(F) = [-y, -xy]and C is the upper half circle arc…

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Q: Use the Lagrange method to find three positive numbers x, y, z such that x+y +z = 90 and x 2 yz is a…

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Q: S F(2,v) For any function f(x, y) continuous on the ry-plane, f(r, y) dædy. O True False

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Q: Verify Stoke 's Theorem for F = (x² +y – 4) î + 3 xyj + (2 xz + z²) k over the surface of hemisphere…

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Q: At what points (x,y.z) in space are the tunctions continuous? a. h(x.y.z) = In (4z² - 4x – 2y³ - 5)…

A: This is a problem of multi variable calculus.

Q: At what points (x,y.z) in space are the functions continuous? a. h(x,y,z) = In (2z - 4x – 5y3 – 1) 1…

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Q: (b) Apply the method of contour integration to prove that (2m de 2n Jo 2+cose 3

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Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: (7) , Find the absolute maximum and absolute minimum of f(r, y) = ya? - y? +4 on the unit disk {(*,…

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Q: Evaluate || F.ndS F = xi + yj+(z² –1)k if and o is the curved surface of the cylinder y = \4-x? from…

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Q: At what points (x, y) in the plane are the functions continuous? ƒ(x, y) = ln (x2 + y2)

A: To find the points in the plane

Q: JSSR xyz dz dy dx = {(xy,z)|(0<x<1),(0<y<1-x),(0<z<2-x)} R= limits 13 а. 240 2 3 100 С. 51 d. None…

A: Explained below

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: The area enclosed between the curves p(a) =2 +*+ 3 and g(@) = -22 - * + is O 16 47 %3D 18 49 O -49…

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Q: Find the absolute maximum and absolute minimum of f(r, y) = yx? – y² +4 on the unit disk {(r, y) : z…

A: Given function fx,y=yx2-y2+4, then finding the critical points we have fx=2xy and fy=x2-2y,then…

Q: ây _ở: x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0. Find the bounded solution of

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Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Find the maximum value of f(x, y) = x°y² for x, y > 0 on the unit circle x2 + y? = 1. %3D fmax

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Q: 4. Evaluate ||| x y dV , where E is bounded by the parabolic cylinders y = x², y' = x and the planes…

A: The region E is bounded by the parabolic cylinders y = x2, x = y2 and the planes z = 0 and z = x +…

Q: (b) Let F = (-yx², xy²). Let D be the annulus 1 < a2 + y² < 4, and let C be its boundary. Evaluate

A: Value of the given integral is

Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

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Q: Solve the problem with Neumann oundary conditions, - Uxx = 0, x, t > 0 u(x, 0) = f(x) ux (0, t) = 0…

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Q: Let S denote the part of the cylinder x2 + y² = 9 that lies between the planes r + y = 1 and x – y =…

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Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z) = In (2z2 – x² – 3y³ – 4)…

A: we want to find the domain of given  function

Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

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Q: At what points (x, y, z) in space are the functions continuous?  a. h(x, y, z) = sqrt(4 - x2 - y2 -…

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Q: a) Evaluate the line integral S. (2x - y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.