: Express the function f (x) = e") to the form u(x,y) + iv(x,y).

Q: (a) Find the points (x ,y, z) in space, where the function f(x, y, z) = Vx² +y -1 Is continuous.

A: It is well known that the equation z=x2+y2 represents a circle with centre at the origin. The…

Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = -√x²+y² is Z- continuous?

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Q: The function f defined by the rule f(z, y) = In(xy) increases fastest in the direction of T. F (1,…

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Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: af Find a d () + In (). of the function f(x,y) = arccot and ду

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Q: Integrate the function f (z) = (z – 8i)- from z = 0 to z = 4 + 4i along the line x = y.

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Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Assuming - 6x° -y² + 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to find…

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Q: A function (f) is homogeneous of degree • if and only if : ôf + y = Af (x, y). Does the function…

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Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: Find a non-zero function h for which F(x, y) = h(x)(x sin y + y cos y)i + h(x)(x cosy – y sin y)j is…

A: Given vector field is, Fx,y→=hxxsiny+ycosyi+hxxcosy-ysinyj.

Q: Dicuss the contiunity of the function f (x,y) = ln  (x+y-1)

A: We know: 1) Polynomials are continuous everywhere. That is, at every point in real number 2) Sum of…

Q: The function f(x, y) = x2 – y² at the point (0,0) is saddle point. صواب İbi

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Q: Find the direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function  fx,y,z=x ln(ey -xz) increases fastest at ( -3, 0 ,0)…

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: (B) Find analytic function f(z) =u +iv such that, d Im dz 2x +e* cos y is analytic function.R x² +y…

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Q: 2. For f(z, y) = z-y, prove that f is differentiable at the point (1, 1).

A: Given: f(x, y) = x2 - y2

Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

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Q: Find the linearization L(x,y) of the function f(x,y) = e (X cos (5y) at the points (0,0) and 0,- 2

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Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

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Q: Find a function f (x, y, z) such that ∇f =〈z, 2y,x〉.

A: Given that, ∇f=z,2y,x We have to find a function f(x, y, z) such that ∇f=z,2y,x. Let us consider,…

Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 4. Find the analytic function whose real part is u(x, y) = e* cos y.

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Q: Find the linearization of the function f (x) = x° 26 at æ = 1. a vā |a| sin (a) L (x) = Using this…

A: I am going to solve the given problem by using some calculus to get the required result.

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

A: Consider the following function: fx,y=excosy Differentiate fx,y with respect to x taking y as…

Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

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Q: Integrate the function f (z) = (z – 8i)² from z = 0 to z = 4 + 4i along the line x = y. 2

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Q: Find whether the function F-(* - y')i + (v² – 3x)j + (=* - xy)k is irrotational.

A: A vector field F is called irrotational if curl (F) = 0.

Q: 6. Let f(x, y, z) = e¬ª cosh y + z and P: (-1,0, 0). Find the derivative of f at the point P in the…

A: Given: f(x,y,z)= e-xcoshy+z.

Q: Find the linearization L(x) of f(x) = cot x at x = 4

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Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

A: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: xY (a) Prove that the function f(x,y) is differentiable everywhere in its do- x² + y? main.

A: Differentiablility: A function z=f(x, y) is said to be differentiable in its domain D if the partial…

Q: Show that the function no-f 0, z = 0 f(2) = { – y* z#0 x2 + y? x² + y² is not differentiable at z =…

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Q: At what points (x, y, z) in space are the functions in continuous? ƒ(x, y, z) = x2 + y2 - 2z2

A: Solution:-  At what points (x, y, z) in space are the functions in continuous? Let (m,n,p) is the…

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Find the linearization L(x,y) of the function f(x,y) = e* cos (9y) at the points (0,0) and ...

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Q: (a) If F(v² – x²,v² – y², v² – z²) = 0 where v is a function of x, y,z show that 1 dv 1dv 1 dv 1 хдх…

A: Using chain rule.

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: xY 2. (a) Prove that the function f(x, y) is differentiable everywhere in its do- %3D x2 + y? main.

A: Solution is given below:

Q: 9. Determine the analytic functions f = u+iv, for which u(x, y) = r³+rg(y), where g is a twice…

A: (9) To Find: The Analytic function f for which the real part is u(x,y)=x3+xg(y), where g is a twice…

Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

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Q: iIm(2) Is the function f(2) = |z² e r analytic at zo = 0 ? %3D

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Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

Q: Integrate the function f (z) = (z - 8i)² from z = 0 to z = 4 + 4i along the line x = y.

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Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

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