Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³ with a(t) = (t, cos(3t), sin(3t)). (2æ² + y² + z²) ds =
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![Evaluate the unoriented line integral
(2æ² + y² + z²) ds
along the parametric curve a : [0, 1] → R³ with
a(t) = (t, cos(3t), sin(3t)).
(2æ² + y² + z²) ds =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1bbb03a-1330-4abd-86a4-84230eb34f64%2F8a63fc67-1035-408d-8708-82634d764800%2Fh6vxuc_processed.png&w=3840&q=75)
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- Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces z = x2 + y2 , z = 4 − y at the given point (2, −1, 5).Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following the outline for the triangle from (1,0,0) to (0,1,0) to (0, 0, 1) and back to (1,0,0).Find an equation of the tangent plane to the parametric surface x=5rcosθ, y=4rsinθ z=r at the point (5sqrt2,4sqrt2,2) when r=2, theta=pi/4 z=? should be eqn.
- Let C be the curve of intersection of the two surfaces x³ + 2xy + yz = 7 and 3x²-yz = 1. Find parametric equations of the tangent line to C at (1,2,1).Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces x2 + y2 + z2 = 14, x − y − z = 0, at the given point (3, 1, 2)., Find a standard equation for the tangent plane and parametric equations of the normal line at the point P,(2,1, e) on the surface defined by the equation xIn y+ yln z=x.
- Let r(t) = Find a parametric equation of the line tangent to r(t) at the point (85, - 324, 13.54)Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 - cos u) sin v, u) at the point where u = v= TT IN 2Find an equation of the normal line to the parametric surface given by R(u, v) = ((2+ cos v) cos Tu, U +(1 – u) sin v, (1+ cos v) sin Tu) at the point where (u, υ) (1, π).
- Find an equation for the tangent plane to the surface 4xy® + sin(Tx) Z = at the point (1, 1, 4)a) Find the equation of tangent line of curve that is given by parametric equations x = 3cost + sint y = e2t at the point (3, 1). b) Find the extrema points of f(x, y) = x³ + 6x² + 3y? – 12xy + 9xLet F(x, y, z) = (6xyz+4x) i+(3a²z+ze-")j+(3x²y-e¬³) k, and let C be the portion of the parametric curve given by x = 6 cos t, y = 6 sin t, z = 3+3 sin(11t/2) that starts at (6,0, 3) and ends at (-6,0,0) (see diagram to the right). Calculate %D F. dr. Show your work, and circle your final answer. (-6, 0, 6), (6, 0, 3) x.