Use polar coordinates to evaluate || (2x-3y) dA, R ere R is the region in the upper half-plane bounded by the circles x²+y² = 4 and x²+y² = 9.

Q: Let C be a circle lying in the plane x+ z = 2 with center at (1,0, 1). Evaluate the line integr V2…

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Q: B) Use Green's Theorem to evaluate /F-dr, where C is the circle r² + y? = 4 and F (r, y) = (y – 2…

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Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

Q: b. Consider the region bounded by the same parametric curve as given in (a) but with different…

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Q: Which of the following correctly represents the plane region in the first quadrant bounded by the…

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: 3. Explain what is wrong with the following statement: If R,T are corresponding regions in the xy…

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Q: Under the transformation w = :-1 -find the image of the circle E = 1 in the w – plane.

A: Given : w=z-11-iz ⇒w1-iz=z-1 ⇒w-iwz=z-1 ⇒z+iwz= w+1 ⇒z1+iw=w+1 ⇒z=w+11+iw

Q: 12. Let R be the region of the plane R= {(r, y) : # 2 0 and ²+ y? < 2}. Describe R using polar…

A: Here, the given region is: R=(x,y):x≥0 &amp; x2+y2≤2

Q: Z'+Z=2

A: I am providing the solution of (ii) only. The solution is as follows below:

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: Use Green's Theorem to evaluate - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

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Q: 3. Find the points on the surface z = = xy + 2 that are closest to the origin.

A: Let g(x,y,z) be the constraint function and f(x,y,z) be the function whose extreme values to…

Q: Evaluate | F-dS, where F(x, y, z) = (3y, –2x, –), %3D and S is the surface that is composed of the…

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Q: Let F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F - (b) What…

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