The slope of the tangent line to the curve of intersection of the plane r = zo and the surface z= f(z, y) at the point (zo, y0, 20) where zo = f(r0, yo) is given by o fz(x0,yo) O fy(xo, yo) O fr(#0, y) O fy(z0, yo, zo)

Q: find the tangent plane to the surface z = Vy-x at the point (1,2,1)

A: Equation of tangent plane is z-c = df/dx(x-a)+df/dy(y-b) at point (a,b,c)

Q: Find the points on the surface xy + yz + zx - x - z2 = 0 where the tangent plane is parallel to the…

A:

Q: Find an equation of the plane tangent to the surface xy z = 2 at the point (2, 1, -1). O A.x + 6y +…

A:

Q: The tangent plane to the surface x? + yz +1 = 0 at the point (x, y, z) (2,–5, 1) passes through…

A: The given problem is to find through which point the tangent plane to the surface at given point, we…

Q: The equation of tangent plane to the surface f(x,y, z) x+ y +z-9 0 at the point (1,2,4) is x+y+z=…

A:

Q: Verify Green's theorem in a plane with respect to S. [(x2 - y²)dx + 2xy dy], where C is the boundary…

A: Using greens theorem

Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

A:

Q: Find the plane tangent to f(x,y)=x/(x+y) at the point (1,5).

A:

Q: Find the circulation of F(x, y, z) = (-y sin 2, x sin z, xy cosz +12) around the circle cut from the…

A: Given that,F(x, y, z)=(-ysinz, xsinz, xycosz+12) around the circle cut from the sphere x2+y2+z2=5 by…

Q: Find the tangent plane and normal line to the surface f (r, y) = In (2r + y) at the point (-1,3,0).…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

A: We know that the parametric equation of a tangent line to the curve of intersection of the two…

Q: find the tangent plane to the surface z = y-x at the point (1,2,1)

A:

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

A:

Q: Find the tangent plane to the surface z = cos(3ry) + z' + 2y at the point (1,0). (z = cos(3ry)+z'+…

A:

Q: ns: Find the tangent plane to the surface of x2 + z² = y² + 9 at (1, –1,3). 3

A: Follow the procedure given below.

Q: Determine if the surface x^2 + y^2 +z^2 = 1 is tangent to the surface x^2 + y^2 + z^4 = 1 at…

A:

Q: 3. Give an example of a surface defined by a function F(r, y, 2) k such that the tangent plane to…

A: Equation of tangent plane of the function, F(x,y,z) at the point (x0,y0,z0) is  Fx =…

Q: The equation of the tangent plane to the surface f (x,y,z)= xe" cosz- z-1= 0 at the point…

A: Given surface is xeycosz-z-1=0 and the point is A1,0,0 find the equation of tangent

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: Find the tangent plane to the surface z= ( x cos(y)) - ye^x at the point (0,0,0).

A:

Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = ln (x2 +…

A: Given z=ln(x2+y2)

Q: Find the slope of the tangent line at (-1, 1,5) to the curve of intersection of the surface z = x²…

A: According to question, we have, z = x2 + 4y2        .......(1)

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: 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: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

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 on the surface f(x,y)=x+y2+xy-24x+2y at which the tangent plane is horizontal.

A: We have to find the points for horizontal tangent plane.     According to our guidelines , We can…

Q: The equation of the tangent plane to the surface defined by z y exp(-x) at the point (0, 1, 1) is =…

A: equation of the tangent plane

Q: = xyz exists over a surface S c ed by the plane x-0,y%3D0,z%3D0, z=y V dS over the curve surface.

A: Given:  V= xyz x2+y2=9 To find: ∫s V ds  For solving the convergence x2+y2=9 (mod 1s) we use Chinese…

Q: Let F(r, y, z) = 2x² + 14y? + 722. Find the equation to the tangent plane to the level of surface…

A:

Q: The slope of the tangent line to the curve of intersection of the plane x = xo and the surface z =…

A: Proceed as shown below

Q: Find the equation of the tangent plane at the point x = xo = 4, y = yo = 1 of the surface %3D z =…

A: Option C is true

Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Find an equation of the tangent plane to the surface f(x, y, z) = x 2 + y 2 + xy − yz − xz + z 2 − 2…

A:

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

A:

Q: Calculate F. dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: We have to find double integral of F. ds

Q: The tangent plane and the normal line of the surface x = y? + z2 + l at (3, 1, -1) have the…

A: Solve the following

Q: Find the tangent plane at the point (1,-1,1) of the surface f(x,y,z)= x^2y+y^2z+z^2x. %3D

A:

Q: Give an arclength parametrization of the line which is the intersection of the tangent planes of…

A: Let First, find the tangent planes at (1, -1, 0), (1, 2, 9).     Tangent plane at (1, -1, 0):…

Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = 1/ (x2 +…

A: Concept - Equation of plane is given by - Ax-x0+By-y0+Cz-z0 = 0         ...............(1)where,x0,…

Q: If the tangent plane to the surface z = +y is parallel to the plane r+ 2y-z 0 at the point (1, a,…

A:

Q: Find an equation for the plane that is tangent to the surface z = vy-x at the point (1, 2, 1).…

A: To find an equation for the plane that is tangent to the surface at the given point (1,2 1).

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

A:

Q: the tangent plane of the surface [ z=x^5+e^(xy)cosyx] at the point (1,0) O z=5x-y-3 O z=5x+y-3 O…

A: Above question is solved.

Q: the tangent plane of the surface [ x^2+y^2+z^2=14] at the point (1,3,2) O 3 x-6y + 4z = 28 2x+6y-4z…

A: Given problem:- the tangent plane of the surface [ x2 +y2+z2=14] at the point (1,3,2)

Q: Find the plane tangent to the given surfaces at the specific point. f(x, y) = ex(x cos y − y sen y)…

A:

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

Q: Calculate / F . dS where F = (e* sin y, e cos Y, yz²) S is the surface of the box bounded by the…

A:

Q: Find the tangent plane and normal line of the surface x+y+z=1 at the point p(0,1,0).

A: