1 Let S be the surface parametrized by r(u, v) (u cos v, u sin v, 9- u- -u²), for 0

Q: Find an equation of the normal line to the parametric surface given by R(u, v) = ((2+ cos v) cos TU,…

A:

Q: Compute the work done by the force 7 = (sin(x + y), xy, x²z) in moving an object along the…

A: Given force The object is moving along the straight line and from

Q: Find the tangent plane to the equation z = z = 3x² + y² + 4y at the point (1, 0, 3)

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A:

Q: x² + y³. 2 = Consider the surface S of equation (1, 1, v), An equation for the tangent line tangent…

A: We have to find the equation of tangent line.

Q: Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 -…

A:

Q: B) r(t) = (4 cos t, 4 sin t, 16)

A: We consider x=rcos(theta) and  y=rsin(theta)  Therefore r^2=x^2+y^2

Q: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: The differentiable function f(*, y, z)= 1x² +7y +3z +4xyz tangent vector v, with i = (1,2,3) e R',P…

A: We have to calculate the derivative of f

Q: g(x,y,z)=x^2+y^2+(z-3)^2

A: For (a), We need to find the equation of the tangent plane to the level set g(x, y, z) = c at the…

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

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

A:

Q: Consider the function f(r, y) = e=² sin( q² + y²) (a) ) Compute the gradient of f. (b) 1 ) Find the…

A: Given fx,y=e-xsinx2+y2

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

A:

Q: directional deriva

A: