The area below the graph of f(x) = and above the x-axis, on the interval [0, 8], is to be rotated about the x-axis, to generate a solid. 3

Q: 3.Find [, (3x² + y)dydx -2

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Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

A: To solve the line integral ∫(2x - y)dx + (x + 8y)dy over the curve C, which is the x-axis segment…

Q: Evaluate 112 (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 2

A: To evaluate the given line integral

Q: The plate, bounded by the parabola y = x² and y = 16, is submerged vertically in water (distance in…

A:

Q: Find the maximum value of the function f(x, y) = xye-(²x+3) in the first quadrant.

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Q: Show that ƒ(z) = 3x² + 2x − 3y² − 1 +i (6xy + 2y) is differentiable at every point in the plan -

A: The given function is f(z)=3x2+2x-3y2-1+i(6xy+2y)...(i).

Q: y? x² 4 Find dV , where E is the solid y2 x2 + 4 z2 - <1. 9 + +

A: First we have Choose suitable parameters.

Q: What is the domain of h(x, y) = Vx - y?

A: Given: hx,y=x-y we know that for domain of square root function inside of root not has to be greater…

Q: The temperature at a point (x, y) on a rectangular metal plate is given by T(x, y) = 100 - 2x2 - y2.…

A: Given: T(x,y) = 100-2x2 -y2We have to find the path a heat-seeking particle will take, starting at…

Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

Q: Find and sketch the domain of the function f(x,y) = cosx + V3x-y+2

A: The given function is .The objective is to find the domain of the function and sketch the domain.

Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: Evaluate f" Na-*) /x² + y² dydx, using polar coordinate. -a

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

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Q: Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 4 and z = 5xy.…

A: Use hyperbolic functions to parametrize the intersection of the surfaces  and (Use symbolic notation…

Q: Coute : 2y da + 3x dy, where D is described by 0 < a < 1, 0 < y < 1.

A: We have to find the given integral. For this we can use Green's theorem

Q: Usefe x dy - y dx to compute the area of the ellipse ()² + ()² = 2 = 1. (Use symbolic notation and…

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Q: A particle moves in the xy plane so that at any time -2 ≤ t ≤ 2, x = 3 sint and y = t - 4 cost + 1.…

A: A particle moves in the xy plane so that at any time ,  and .What is the vertical component of the…

Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

Q: Use hyperbolic functions to parametrize the intersection of the surfaces x² - y² = 25 and z = 5xy.…

A: Here we have to parametrize the surface using hyperbolic functions.

Q: 16. (2+) y dy

A: