2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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A:

Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

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Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) > 0.

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A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

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Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

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A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

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Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

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Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

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Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: Find and classify the critical points of f(x,y) = 4r+20² - y²

A: Find and classify the critical points of f(x,y)= 4x+2x2-xy2.

Q: Let f (x, y) = r³ + y? – critical points of f . 4xy + 3x + 2y+5. Find and classify all

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Q: Find and classify the critical points of f(r, y) = 2y²x- ya? + 4yx.

A: Here we have to find and classify the critical points of f(x,y) = 2y2x - yx2 +4yx .

Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

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Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

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Q: -2 In(x) Consider the function f(x, y) 3y

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Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

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Q: Find the linear approximation 0 to Write your answer in the form y = Ax + B. at x =

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Q: Where does the function f(x,y)=3 − 10x + 12y − 5x2 − 6y2 have a critical point?

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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…

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Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.