The intersection of the ellipsoid x? + 4y? +z? = 36 with the plane z = V3x gives an ellipse C. A) Write a parametrization of this ellipse r(t) for 0 sts2x. r(t)= (]cost,sint, cos t). B) In order to do the line integral of the function 4 f(x,y.z) =, 16 36 36 over this ellipse one must find the integral of (enter the appropriate number in each term which appears in the integrand) 2x f ds = ] JOsin ?t +O cos ?t) dt

Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: 6. The ellipsoid + y2 + z2 = 4 and the plane y = 1 intersect to form an ellipse. Find slope of the…

A: Given:

Q: Use Trapezoidal Rule to find the lower bound m and the upper bound M of the value of the integral…

A: To Find: Upper and lower bounds for the integral I=∫12lnx dx using trapezoidal rule such that error…

Q: x² Q 6) Find the equation of the tangent to the ellipse y² = 1 at the point (xo, Yo)

A: To find the slope of the tangent at (x0,y0) we find dy/dx and put x=x0 and y=0 in it

Q: Determine the surface area of the solid obtained by rotating the following parametric curve about…

A: Given: x=9+t2, y=2t, 0≤t≤2

Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

A:

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: Find the equation of the plane tangent to the surface z = 3x² + y² at (1, 1, 4).

A:

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and…

A:

Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = = sin 0, 0 E…

A:

Q: Write an equation of the tangent plane to the ellipsoid (a – 5)? + 4y? + 222 : М(5, 3, 1). = 38 at…

A:

Q: Consider the ellipsoid 4x2 + 2y2 + z² = 27. Find all the points where the tangent plane to is…

A: We have to find the points.

Q: tangent plane at the point (-2,1 – 3)

A: Equation of the tangent plane = dfdxx-x0+dfdyy-y0+dfdzz-z0 Let f=x24+y2+z29-3 (given)

Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

A:

Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

A:

Q: (-3x) dxtxdy C is part of the ellipse 5x2+6y=30 fromC0,-V5) to cra,O). X,

A: Line integral Given ellipse is  From .