4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) = u²i + 2u sin vj + u cos v k %3D at (1,0, 1).

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

A:

Q: (4) The equation of the tangent plane to the surface In = z²(x – 2y) + 3z +3 at (4, 2, –1) is 2y

A:

Q: Find an equation of the tangent plane to the surface S : za? – xy – yz = 18 at the point (0, –2, 3).…

A: We know that an equation of the tangent plane to the surface Fx, y, z at the point x0, y0, z0 is…

Q: Given the surface z = In(-2x² + 5y² – xy). Find the directional derivative of the function f at…

A:

Q: The horizontal tangent plane of the surface z = 4x – xy – 2y – 2x – 8y – 3 is given by the equation…

A:

Q: Consider x=h(y,z) as a parametrized surface in the natural way. Write the equation of the tangent…

A:

Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

A:

Q: Let F(x, y, z) =7x2+8y2+13z2. Find the equation to the tangent plane to the level of surface F(x,…

A:

Q: Find an equation of the tangent plane to the surface z=−2x^2+3y^2−x+3y+1 at the point (1, 1, 4)…

A: We have to find the  equation of tangent plane

Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Find the surface area of the solid obtained when the parametric curve x = −2cost; y=2sint for 0 ≤ t…

A:

Q: Find equation of the tangent plane to the given surface at the specified point. 5x^2+3y^2+8z^2,…

A:

Q: Find the plane tangent to the given surfaces at the specific point f(x, y) = x2 ln(2x+y) in (-1, 3)

A:

Q: Find an equation of the tangent plane to the surface x2 + 2y? + 3z2 = 6 at the point (1, 1, 1). O A.…

A: As we know that the equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 Given:…

Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

A:

Q: Are there any points on the hyperboloid x 2 − y 2 − z 2 = 1 where the tangent plane is parallel to…

A:

Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

A:

Q: Find the equation of the tangent plane to the surface z = In (2x + y) at the point (-1, 3, 0) . O x…

A: The equation of the tangent plane to the surface Z=fx,y atthe point a,b,fa,b is given by…

Q: Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the…

A:

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Find the plane tangent to the surface z = x cos y - yex at (0, 0, 0).

A: Consider the following function: z=fx,y=xcosy-yex Differentiate function fx,y with respect to x:…

Q: Find the point (x, y, z) on the surface z = 2x2 - y where the tangent plane is parallel to the plane…

A: We have to find the point (x, y, z) on the surface z = 2x^2 - y^2 where the tangent plane is…

Q: Exercise (2): Calculate fe xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to…

A: we have to following integral

Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

A:

Q: 9. Show that the sum of the T-, y-, and z- intercepts of any tangent plane to the surface VI + Vỹ +…

A: Given, Gradient of the surface at any point (x0,y0,z0) is given by,

Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). %3D

A: Given that XY3 Z2 =2 And point (2, 1,-1).

Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

A:

Q: Find an equation of the tangent plane to the surface given implicitly by z= sin(zy) at the point (,…

A: A tangent plane to a surface is a plane that just touches the surface at a single point. The…

Q: 9) Find a point on the surface z = 8 – 3x2 – 2y² at which the tangent plane is perpendicular to the…

A: Given, Surface, z=8-3x2-2y2 at which the tangent plane is perpendicular to the line…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

A:

Q: Find the points on the surface 1x^2+2y^2+5z^2=1 at which the tangent plane is parallel to the plane…

A:

Q: Find the equation of the tangent plane to the surface 3D1 16 at the point (1,-3,2) O a. 2x+4y-3z=12…

A:

Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)

Q: Find the equation for the tangent plane to the surface z=In(9x2 + 5y2+1 O x+y = 0 z = 0 O x-y = 0 O…

A:

Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z = (xy)^1/2,…

A: We know that tangent plane to the surface z=f(x,y) at point (a,b,c) is

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – z2 O y…

A:

Q: 30. The equation of the tangent plane to the surface z = x? – 2y² at x = 1, y = 0 is (а) 2 — : 2т —…

A:

Q: Determine the equation of the tangent plane to the surface z=x - 3xy + y at the point P (2, 1, 3).…

A: Solution

Q: At what point on the ellipsoid 2x^2 + y^2 + z^2 = 1 is the tangent plane parallel to the plane x + y…

A:

Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

Q: Find the equation of the tangent plane Pr to the surface S:r +y +z2 = 9 at (2,-1, 2) | O PT:4x + 2y…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Find the equation of the tangent plane to the surface xy + 2yz + 3zx = 11 %3D at the point P (1, 1,…

A:

Q: Are there any points on the hyperboloid r² – y² – 2² =1 where the tangent plane is parallel to the…

A:

Q: 13. Find all points on the surface at which the tangent plane is horizontal. 3,,2 (a) z = x°y ² (b)…

A:

Q: 2. Find the area of the surface obtained by rotating the curve: y = Vx +1,1<x<5 about the Х-ахis

A:

Q: 14. Find a point on the surface z = 3x- y at which the tangent plane is parallel to the plane 6x +…

A: