Verify Stoke 's Theorem for F = (x² +y – 4) î + 3 xyj + (2 xz + z²) k over the surface of hemisphere x² + y² + z? = 16 above the xy-plane.

Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

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Q: 2) Draw contour maps for functions f(x, y) = x² - 4y², and g(x, y) = x² + 4y². What shape. are these…

A: The contour of function f(x,y) represents parabolas.

Q: calculate ∫Cy(x-z) ds, where C is the intersection of the surfaces x2+y2+z2=9 x+z=3

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Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: sin(7y), 8x2+7x°cos(7y)). vative servative n of the parabola y=x2-16 from (4,0) to (-4,0). Which of…

A: We have to choose the option

Q: Describe the level surfaces for f (x, y, z) = y+10-√√x² + z² and sketch them for several (at least…

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Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Describe the level surfaces for f(x, y, z) = y+10-√x² + z² and sketch them for several (at least two…

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Q: Describe and sketch the following surfaces z = f(x, y): (a) * (c) 2= /1-x² - y² z = 6 - 2x - 3y (b)…

A: We have to sketch and describe the following curve

Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: Find the points on the surface 1x² + 1y² + 3x² = 1 at which the tangent plane is parallel to the…

A: We know that two planes are parallel if their normal vector are parallel. That is their, gradient…

Q: Consider f(r, y) = /1– 2² – y². (a) What is the domain of f ? That is, for which (r, y) does the…

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Q: Evaluate F. dr where F(x, y) = x²y² + 2xyj and C is the boundary of the square (clockwise) through…

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Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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Q: V=R Prooflthat Nisavectors sPoe

A: Given that V = ℝ+ Operations + and · defined as, x + y = xy rx = xr, where x,y ∈V; r ∈F To prove: V…

Q: 9:25 م Pll حل مثال تحليلات....p ح (400 36 ة ميويود + ہے - ... [73] ك Laplace ex

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Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: Find an equation of the plane tangent to the surface z = x2 + y2 at (2, 3, 13). [Hint: Consider the…

A: Note: Here, f(x,y,z) = x2 + y2 - z and the point is (2, 3, 13).

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: Let z = V162 – 4x? – 9y?. (a) Find the domain of f(x, y) in R?. (b) Sketch the contour map of f(x,…

A: Domain: The domain of a function z=fx, y of two variables is the set of those points  x, y in the…

Q: The domain is the entire xy-plane.

A: Domain -Domain constitutes only the values of x on which the function is defined.

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: Calculate |E F.dr, where F(aа, у) — (2? —Зу)і+(ye®)j and the сurve and curve ' is the parabola х %3D…

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Q: Cis the semicircular curve drawn in the ground (the xy-plane) joining the points (0, - 2), (2, 0),…

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