Express the function f(z) = sin(=) in the form f(z) = U (x, y) + V (x, y)i. %3D

Q: Find the differential and evaluate for the given x and d/x of the function, y = tan x, x = 0, dx =…

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: Find the differential of the given functions. a) f(x) = sin(cos(22)) CoS %3D 2x b) g(x) x3 – 7x

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Q: b) Find the potential P(x,y) attached to the exact ODE 2r sin(y) + x* cos (y) y = 0

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Q: Write the differential dw in terms of the differentials of the independent variables. w = f(x,y,z) =…

A: Hair we have to find out the differentials

Q: Find the differential of the function y = f(x). f(x) %3D X - 8 dy = %3D

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Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

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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: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

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Q: define y as a differentiable function of x,  find the value of dy/dx at the given point. 25. x2 + xy…

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Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

Q: The differential of the function f(x,t)= e cos(2 tt) at the point (x,t)= (0,1) is given by -2dx +2…

A: Topic- Application of derivatives

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Q: The function f (x, y) = e÷ + 3 tan is a homogeneous function of what degree.

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Q: Let y = 3x2. Find the change in y, Ay when x = 2 and Ar 0.2 Find the differential dy when x = 2 and…

A: We have to find solution

Q: define y as a differentiable function of x,  find the value of dy/dx at the given point. 25. (x3 -…

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Q: Find the differential of the function y= 1/√(u^2+v2), where u and v are differentiable functions of…

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Q: 3. Integrate the function. (a) / Vx–1dx = %3D (b) /e2+ 2x+1 dx = (c) | (sin xcosx+ sinx cos x) dx =…

A: Hello there! You seem to have uploaded a question with multiple subparts. As per our guidelines, we…

Q: Write the differential dw in terms of the differentials of the independent variables. w = f(x.y.z) =…

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Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate  dy and ∆y if x= and π /4 and dx =-0.1.

A: Given function is (a) Differentiating with respect to x, we get

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A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: Find the (absolute) maximum and minimum values of f(x, y) = sin x cos y on the square R = {(x, y)|0…

A: Given,            f(x, y)= sinxcosy                    (1) on the sqaure             R=x, y| 0≤x≤2π,…

Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: Let y = 3Ja. Find the change in y, Ay when x = 3 and Ar 0.2 %3D Find the differential dy when x = 3…

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Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

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Q: F(t, x, y, 2) = [0, cos(t), sin(t)] x 7, 0<t<

A: Solution

Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: Find fa, fus and fz. f (x, y, z) = (5z)) 3z In (x*y cos

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Q: 31. f(x, y) = e cos y a. (0, 0), b. (0, п/2) %3D at

A: We know that linearization of f(x,y) at (a,b) is

Q: Let y = f(x), where 3x? f(x) : Зx + 4 ,2 x + 4 Find the differential of the function. dy =

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Q: B sin x Find an antiderivative F(x) of the function f(x) such that F(0) = 1. y + cos x

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Q: Write the differential dw in terms of the differentials of the independent variables. w =…

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Q: B sin x . Find an antiderivative F(x) of the function f(x) such that F(0) = 1. Y + cos x

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Q: (a) Find F'(x), where (i) F(x) =x t cos(12) dt; %3D (ii) F(x) = sin(e") ds. %3D

A: Solution of question as follows

Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Linear measurement is one-dimensional. A linear differential equation is an equation where the…

Q: h of the DE's =)y = 2 sin² x ; y(0) = 0 , y'(0) =-2

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Q: Find the differential of the function. Z = e-9x cos(2rt) dz = dx + dt %3D

A: The total differential of the function  is given by . So, to find , first we need to find the…

Q: 3. Find the derivatives of y with respect to x: a) y = xe* - e* %3D b)' y = e(+x+2) c) y = e*(sin x…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Using linear approximation, estimate e^0.1 cos(0.1)

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Q: ind the linear approximation of the function at the given point. x_ v) = -4 sinx+ 7 cos y at (0, 7…

A: Hey, Since you have posted multiple questions we will answer only first question.

Q: x²+y²` du du =+y dx If u=sin| ,x+y #0,Prove that x =tan u x+y dy

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Q: F(x) = [,**dt COS x 1 %3D 19

A: Answer is given below

Q: Find the differential of the function. Z = e-8x cos(5xt) dz z = dx + dt %3D

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Q: e of the function g(x y, z) = 1/xz + e%.

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Q: Use the Chain Rule to find dw where w = sin 8x cos 2y, x = , and y = t°. dt 2 dw dt (Type an…

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Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: implicitly dx

A: Solved below