9. Show that the sum of the T-, y-, and z- intercepts of any tangent plane to the surface VI + Vỹ + VE = vc is a constant.

Q: If (a,ß.r) is a point at which the surface x2+y2-z-2x+42=0 has a horizontal tangent plane, then Iyl=

A: Horizontal tangent plane

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

A:

Q: Find the point(s) on the surface z = x2 − xy + y2 − 2x − 2y, at which the tangent plane is…

A:

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

A:

Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: B Suppose we want to find all the points on the surface gx, y) x+ 4y - 4 where the tangent plane is…

A:

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. cos…

A: Given,

Q: Find the points on the surface x2 - zy = 4 closest to the origin.

A:

Q: Consider the normal line to the surface z = x2 + y² (paraboloid) at the point P(1, 1, 2). Find the…

A:

Q: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

A:

Q: Suppose that an equation for the surface is S(x,y) = xye^x. In what direction (relative to the…

A:

Q: Q4) given the surface: cos nx – x²y + exz + 2yz = 2 Find the equation of the tangent plane and…

A:

Q: Find the points at which the following surface has horizontal tangent planes: x² + 2y² + z2 – 2x –…

A:

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

A: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

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: Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the…

A:

Q: Find the points on the surface ry + yz + zx – x - 22 = 0 where the tangent plane is parallel to…

A: Given surface is  Fx, y, z=xy+yz+zx-x-z2 and we have to find the points on this surface where the…

Q: 1. Find the closest point of the surface ry + xz + yz = 1 to the origin. %3D

A:

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

A:

Q: The equation of the tangent plane to the surface X +y- z = (2, –1, -1) is 2 at the point | O a) None…

A: This question can be solved by applying the formula of equation of tangent plane to the given…

Q: Consider the surface x2 + y2 − 2xy − x + 3y − z = −4 and the point P(2, −3, 18). Determine the…

A:

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

A:

Q: 9) Find a point on the surface z= 8 – 3x² – 2y² at which the tangent plane is perpendicular to 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 sum of the x-intercept, y-intercept, and z-intercept of any tangent plane to the surface…

A:

Q: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

A:

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Find the point(s) on the surface z = 3x2 + 2y2 − 3x + 4y − 5, at which the tangent plane is…

A:

Q: Show that the surfaces x2 + 2y2 + 3z2 = 3,   x2 + y2 + z2 + 6x − 10y + 14 = 0, are tangent to each…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Let C be the curve of intersection of the parabolic cylinder x = 2y, and the surface 3z = xy. Find…

A:

Q: 4. Determine all points on the surface x² + 2y² + 3z² + 2xy + 2yz = 1 in which the tangent plane of…

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 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 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: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

A:

Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

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: Write the equations of the tangent plane and the normal line to the surface y + In(xz) Z = at the…

A: I have appended the formula used in the solution part

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 to the given surface at the point (0,-1,2). y = 2x2 – 2 - O y…

A:

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

A:

Q: Find the points on the surface xy – z2 = 1 that are closed to the origin.

A: Given surface is xy-z2=1. let xy-z2-1=0⇒z2-xy+1=0 Now distance from origin is…

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: