Calculate | [(a4 – 3y) da + (2y³ + 4.x) dy] wherein r(t) = (3cos(t), 3sin(t)), 0

Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

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A: The solution is given in the next step.

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

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Q: Let a, b be positive real number, F = (esinx + y) i+ (3x – 4(tan y) )j, and C be the boundary of the…

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Q: 4. Where does the curve r(t) = ti + t²j+ (3 t2)k intersect the paraboloid z = x2 +y² ?

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Q: F = [y3,n3] 4 c is the Parrabola y - sa2 from A (0,0) +0 Bl2,20) SF.di = Syoda tao dy y=5a2 Since y…

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Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

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A: We will use parametric equation of ellipse to find line integral . As only one question allowed to…

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Q: The attached figure shows the surface S1: y + z= 2, limited in the first octant with surface S2: x =…

A: The area of a surface z=f(x,y) bounded by the region R is given by the integral expression:-…

Q: Find F. dr, where F(x, y) = (xy² + cos x)i+(x²y+sin y)j and C is the ellipse C x2 + 2y2 = 9,…

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Q: Find a parametrization of the paraboloid given by f (x, y) = x 2 + y2.

A: To find a parameterization of the paraboloid given by: fx,y=x2+y2

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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: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &3, x2-y2=3 &4 Where u=xy and v=x2-y2

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Q: Let C be the boundaries of the ellipse +=1 taken in the 9 16 counterclockwise direction. A…

A: We have to check

Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder x² + (y − 1)² = 1.…

A: For the given curve we have the following vector valued function: R⇀=2cost. 1+sint,…

Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: Calculate | [(a* – 3y) dæ + (2y³ + 4x) dy] wherein y(t) = (3cos(t), 3sin(t)), 0 <t < 2ñ, is an…

A: Please check step 2 for the solution.!

Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: Find the surface area of the portion of the part of the paraboloid z = 3 – x² – y² that lies above…

A: Given z = 3-x2-y2 , above the plane z=-1

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A: Converting into spherical coordinates

Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

Q: 11. Evaluate ([(y+z³ )dS where S is the part of the paraboloid x = 4- y – z² that lies in front of…

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Q: Let F (tanx + y)ĩ + (x + secy)j and C be the boundaries of the ellipse 9y=9 in the counterclockwise…

A: Given - F→ = tanx + yi^ + x + secyj^ and C be the boundaries of the ellipse x2 + 9y2 = 9 in the…

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Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: What is the equation of the plane to the surface z = e3Y sin(3x) +2 at the point P,0, 3) O x- y + ez…

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Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

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Q: Find the maximum and minimum values of f(x, y, z) = x - z on the ellipsoid x² + 2y? + 22 = 1.

A: maximum=? minimum=?

Q: Let o(r, y, 2) = x2 + (y/2)2 + 22. Find the point on the ellipsoid o = 1 closest to (1, 1, -1).

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Q: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: Evaluate (any way you want) the integral fF.dr, y² x=3 4 9 oriented counterclockwise, and F(x, y, z)…

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Q: Use Lagrange multipliers to find the maximum and minimum of f(r, y, z) = -r + 2y + 2z on the ellipse…

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Q: Q– Fin the surface area of the portion of the paraboloid z= 6-2x - y that is above the x-y plane…

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Q: Is it true or false that by using a suitable translation x = x' + xo, Y = y' + Yo, it is possible to…

A: Transforming the conic equation

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A:

Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x² + y2? (If an…

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

Q: Are there any points on the hyperboloid x² – y² – 2² = 1 where the tangent plane is parallel to the…

A: By see this solution

Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

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Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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