Compute the area of the surface formed when f(z) 2V1-z between -1 and 0 is rotated arou nd the -axis. otating f(r) VT around the r-axis.

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: - Find div F and curl F if F(x, y, z) = 10y¹z7i – 17xªzºj – 3xyễk. div F= curl F=

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: The density of deer in a forest is the radial function ρ(r) = 150(r2 +2) −2 deer per square…

A:

Q: n exact form. Use symbolic notation and fractions where needed.)

A:

Q: An airport is located at D(0,0). A plane is currently positioned at C(-9, - 16). The radar system at…

A:

Q: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x + 56. Use the…

A: The region is bounded by the graphs fx=x2 and gx=-x+56. We have to find the centroid of the region.

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

A:

Q: Determine the expression for Fyz(x, y, z) given the function F(x, y, z) = 2x²y – xz? 3y z.

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Q: Sketch the surface x = 2y2 +3z2

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Q: Find the analytic function if the imaginary part is (2xy + 5y) where u (0,0) = 0

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Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: the doi n ain of the functions

A: We have given two functions : f(x,y)=1xy…

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: V4–x² – y² Let f(x,y) =- Shade the region in the x-y plane that corresponds to the domain of f(x,y)…

A: We are given the function f(x, y)=4-x2-y2lnx-y. For f(x, y) to be defined, we must have the domain…

Q: Evaluate SF-d F=(x² + y²)i-2xy j clockwise in the xy-plane x=0, x=4 and y=0,y=2. and C is the F-dr…

A: We know, for a force F→=P,Q, the line integral ∫CF. →dr→ is given by ∬(∂Q∂x-∂P∂y)dA, according to…

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2