Q5// If F = 3i + 2j – 2xk , Evaluate f. F dv where V is region bounded by the plane y=0,z=0, z=4-y (z 2 0) and the surface x² + y? = 16 %3D

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 a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

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Q: 2 y = 12 – 3x", y = 4 – x 2

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Q: Find the points on the surface y² = 16 + xz that are closest to the origin. smaller y-value (x, y,…

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Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: X- An ant is moving on the surface z = x² + xy + y² such that its - and y-coordinates satisfy cost,…

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Q: c. Locate center of gravity

A: c) Given curve is

Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

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Q: 2 y = 2x – x¯, y = 2x² – 4x

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Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: Evaluate √ √R 6xy5 dydx R where the region is bounded by the curves y = = x² 1 and y = 1-². Sketch…

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Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3