Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region (traversed counterclockwise) in the first quadrant bounded by y = x2 and y = 4.

Q: Evaluate f(x, y, z) dV for the function f(x, y, z) = xz² and region B = [0, 3] × [5, 7] × [4, 5].

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Q: 3. Let C be the part of the circle with radius 3 in the first quadrant as in the picture. 3. (a)…

A: To solve the following paramteric equation problem

Q: Find the absolute minimum value to the nearest integer of f(x,y)=2+ 2x + 2y -x² - y² on the…

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Q: Find an absolute extrema of f(x,y)=2x² - 4x + y² - 4y +1 on the closed triangular region bounded by…

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Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

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Q: Suppose F(x,y)=. Use Green's Theorem to calculate the circulation of F around the perimeter of the…

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Q: Use a substitution of u = r to integrate : dr.

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Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: Let F(x, y, z) y³ 2:5 . What is the value of div F at (1, 2, 3)?

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Q: f(x,y) = x=y - 2xy? + 3xy +4 %3D

A: Given function is fX,Y=X2Y−2XY2+3XY+4 We have to find the global maximum and minimum of this…

Q: Find || (x, y) dA where f(x,y)=y and Ris the region bounded by y = x² and y = x. (A) (c) (B) 12 15…

A: Given: I=∫∫Rfx,ydA ; fx,y=y And y=x2 & y=x   As we know that; The Power rule: ∫xndx=xn+1n+1+C ;…