1. Computer° (x2 y222)1/2 dV, where E {(r, y, z) 0, y < 0, z > 0, 4 < 12 + y2 z2 < 16) E

Q: 16) Which function will shift y= vx right 4 units and up 1 unit? A) y = Vx + 4 +1 B) y = Vx + 1 C) y…

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Q: B) dy = 8xex2. 9) y = e4x² + x A) dy = 8xe2x + 1 dx B) dy = 8xex2 + 1 %3| C) dy = 8xe + 1 D) dy -…

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Q: (3 (x+y+2)dy dx dz

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Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: 4. Compute , 3x – V1 – x² dx.

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Q: Evaluate S xy dx + (x + y)dy along the curve y = 2x² from ( − 3,18) to (-2,8). с Sxy dx + xy dx + (x…

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Q: 3 For f(x,y) = In x+y°, 4,8)

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Q: 20. Verify directly that r2 dy dx dx dy 1+x - y Jo J2 1+x – y

A: take Left Hand side ∫23∫02dydx1+x-y the integral can be written as ∫23∫02dydx1+x-y=∫23∫02dy1+x-ydx…

Q: Let g(x, y) = Vx²y². Find 1. g(1, 2) 2. g(4,1) 3. g(2, у) 4. g(x,2) 5. g(w, z – 1)

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Q: 5. Let w = f(u, v), where u = x + y and v = x - y. Show that дw ди дх ду = () - ( ) 2

A: Given, w=f(u, v) where u=x + y and v=x - y To prove: ∂w∂x∂w∂y=∂w∂u2-∂w∂v2

Q: 3 + .2 J(u) 4u + '(u) =

A: Given J(u)=(3u+3u2)(4u+4u)