Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A:

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

A:

Q: 4. C is the centroid of ADEF. Find CX if FX = 10. E Y X C F D

A:

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 +…

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18z on the elipse…

A:

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

A:

Q: 39. Find all points on the portion of the plane x+y+z= 5 in the first octant at which f(x, y, z) =…

A:

Q: 3. Verify that u(x, y) = x² + 4.x – y² + 2y is harmonic and find %3D - a) the harmonic conjugate…

A: See the attachment

Q: Study the analytically of w = L(2) at the points z = 0, z= v2,z = -21

A:

Q: Find the linearization L (x, y) of the function f (x, y) = y/-x at (-9,4). 2 L(x, y) -x+ 3y – 6 3…

A:

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x2 + y2 + 1 at a. (0, 0), b.…

A:

Q: I need help finding the absolute maximum and minimum values of f on the set D.

A:

Q: Find the linearization of f(r, y, z) = x + y² + z³ at the point (1, 2, -1).

A:

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: Find the linearization z = = L(x, y) of the function z = f(x, y) = 3.x2 – y² + 5y at the point (xo,…

A: z=fx, y=3x2-y2+5y and the point is x0, y0=2, 1. Now, f2, 1=322-12+51=12-1+5=16 Now partially…

Q: 2. Use the transformation u = x – 2y, v = 2x + y to find x – 2y 2.x + y Where R is the rectangular…

A:

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

A: It is a short question so i have written the direct answer

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: given that a function f(x,y,z)=x2+y2+z2 we need to find the linearizations of f(x,y,z) at (1,1,1).…

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

A:

Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x3y4 at a. (1, 1), b. (0, 0)

A: Consider the function: fx,y=x3y4 To calculate the derivatives of the given function with respect to…

Q: 48. Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point…

A: Given that: f(x, y, z)=xyz+3

Q: Let f(x, y) = 2x² + 5xy + 2y² + 5x – 5y + 2. Find the linearization L(x, y) of f(r, y) at the point…

A:

Q: Find the linearization of f(x, y,z) = x + y centered at (8,4, 5).

A: Given:fx,y,z=x+y at 8,4,5Formula:Lx,y,z=fx0,y0,z0+fxx0,y0,z0x-x0+fyx0,y0,z0y-y0+fzx0,y0,z0z-z0

Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

A:

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

A: The correct options are  4th option ,i.e. Rez=x∈ℝ and 2nd option. i.e. Imz=y∈ℝ .

Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: Find the linearizations L(x, y, z) of the function at the given points. ƒ(x, y, z) = x2 + y2 + z2 at…

A:

Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

A:

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 linearization of the function at the given point. f(x y, z) = e5x - 3y - 6z at (0, 0, 0)…

A: Linear approximation in three Variables

Q: find the absolute maximum and minimum of the function f(x,y,z)=x+2y on the intersection curve…

A:

Q: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…

A:

Q: Find the linearization of the function at the given point. f(x,y,z) = 10xy + 7yz+ 9zx at (1,1,1) O…

A:

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

A:

Q: Find absolute maximum and minimum values of the function f(x,y) = 4xy – x²y² – xy + 1 in the closed…

A:

Q: Let T(z) = -6z* +z² –1 and U(x) = 2z – 4x + 3. Find T(z) +U(z) %3D OA. -6z4 + 2z3 +z² - 4z + 2 OB.…

A: Let Tx=-6x4+x2-1  and Ux =2x3-4x+3

Q: Evaluate the fuctions at the given values of the independent variablels.   u= f (w, x, y, z)=…

A:

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

A:

Q: Find the linearizations L(x,y,z) of the function f(x,y,z) = 4xy + yz + 3xz at (1,1,1), (1,0,0), and…

A:

Q: 2. Use the transformation u= x – 2y, v = 2x + y to find S x- 2y dA (4) 2.x + y Where R is the…

A:

Q: Let T : R2 → R2 given by T(x, y) = (2x + y, x − 3y), (x, y) ∈ R2. Determine [T]αα , where α = {(1,…

A: We will find the images of (1,1) and (1,2) under the linear transformation T and then write them as…

Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

Q: Find the flux of F = (x - y)i + xj across the circle x2 + y2 = 1 in the xy-plane.

A: Given F = (x - y)i + xj  across circle x2+y2=1

Q: Find the analytic functiopn f (z) = u (x,y) + i ( x, y ) such that u ( x, y)=  4xy3-4x3y+x.

A:

Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

A:

Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…