4 y-2 ) Answer the following questions about the integral ſf f(x, y)dA=ƒ ƒ ƒ (x, y)dxdy and R 20 a function f(x,y) ≥0 Sketch the region of integration R.

Q: Consider F & C below. F(x,y,z) = yzi+xzj+(xy+18z)k C is the line segment from (2,0,-2) to (4,4,3)…

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Q: 65. y = 3x - x3, x = 0, y = 2 are bounded in the first quadrant. Determine its area. % sq. units %3!

A: Given: when y=2, we have 2=3x-x3⇒x=1. Now, dydx=3-3x2. So,            S=2π∫01 1+3-3x22dx  =2π∫01…

Q: Indepen-dent Variable Depen-dent Variable Equation Order Degree z(iv) + z" = -y y' + ay = bt f" + f'…

A: We have to identify the independent variable , dependent variable, order and degree of the given…

Q: yyx² +y? F(x,y) = - is a homogeneous function of degree

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Q: Let a differentiable function g and f(x,y) = g(x²y²), g(4) = 4, g'(4) = 1 be given. Then, find the…

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Q: Consider the function f(x,y,z) = (x+y+z)° on the domain R’. (b) Is f a quasi-concave function? If ƒ…

A: Given: Function f(x, y, z)=x+y+z3 on the domain ℝ3. To determine: Whether the given function is…

Q: Let a differentiable function g and f(x,y) = g(x²y²), g(4) = 4, g'(4) = 1 be given. Then, find the…

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Q: Are the following functions homogeneous? If they are, determined their order. (a) f(y, t) = t^y² +…

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Q: knowing that f(x,y,z) =0 ,find dx/dz if (z=x+y) (dz/dx should be interm of fx,fy,fz)

A: Given: f(x,y,z) = 0 and z = x+y

Q: Sketch the contour map of the function f(x, y) = 4 – Va2 + y? Label the level curves at c= 4, 3, 2,…

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Q: 16. F(s) +

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Q: Calculate the integral of f(x, y, z) = 9x² +9y² + 28 over the curve c(t) = (cost, sint, t) for 0 ≤ t…

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Q: The temperature at a point (x,y,z) of a solid E bounded by the coordinate planes and the plane…

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Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: u(x, y) = e¯ª (cos x cos y cosh y - sin x sin y sinh y)

A: We have to find the analytic function for which the real part is u(x,y)=e-x(cosx cosy coshy-sinx…

Q: Find the total differential of the function f(x, y, z) = 4 ryz2 df ? dx + ? dy + ? dz

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Q: f(x, y) dA with the following R. You can use any integration Set up iterated integrals for order or…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Suppose A is an n × n nonsingular matrix. Prove that there exists a polynomial q(x) such that A-1 =…

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Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0).  For this we use the proper…

Q: Q4) Consider the function f(x,y,z) = x³ – xy² – zy a) Find the derivative of f(x, y, z) in the…

A: Given function fx,y,z=x3-xy2-zy a) Directional derivative, D=∇f·A⏜…

Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

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Q: Test for an extremal of the functional F[y(x)] = |,´(y'² - y?)dx, y(0) = 0, y = 1 2 0,

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Q: xy2 Let f(x, y) = {x² + y+ 0, (x, y) = (0, 0) (x, y) = (0, 0). Show that f,(0, 0) and f,(0, 0)…

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Q: Then, write a function f(z) such that a) it is analytic in C except its isolated singular points,…

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