Question

Find the equation for the tangent plane to the surface

xy + yz + zx = 11 at P(1, 2, 3)

Answer #1

Find an equation of the tangent plane to the surface given by
the equation xy + e 2xz+3yz = −5, at the point, (0, −1, 2)

1. a) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the tangent plane at (1, 1, 1).
b) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the normal line to the surface at (1, 1, 1).

Find an equation of the tangent plane to the surface z = x^2 +
xy + 3y^2 at the point (1, 1, 5)

1)Find an equation of the tangent plane to the surface given by
the equation xy + e^2xz +3yz = −5, at the point, (0, −1, 2)
2)Find the local maximum and minimum values and saddle points
for the following function: f(x, y) = x − y+ 1 xy .
3)Use Lagrange multipliers to find the maximum and minimum
values of the function, f(x, y) = x^2 − y^2 subject to, x^2 + y 4 =
16.

Find the equation for the tangent plane to the surface
z=(xy)/(y+x) at the point P(1,1,1/2).

Find the equation of the tangent plane of the surface implicitly
defined by xy^2z^3=8 at the point (2,2,1).

(a) Find an equation of the plane tangent to the surface xy ln x
− y^2 + z^2 + 5 = 0 at the point (1, −3, 2)
(b) Find the directional derivative of f(x, y, z) = xy ln x −
y^2 + z^2 + 5 at the point (1, −3, 2) in the direction of the
vector < 1, 0, −1 >. (Hint: Use the results of partial
derivatives from part(a))

1-Find partial derivative of zx for
zcosz=x2y3+z
2- Find tangent plane eq. to the surface zx2+xy2+yz2=5
at the point (-1,1,2)
3- Find all critical points of
f(x,y)=xy2-x2y2+x4+3.

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

Find an equation of the plane tangent to the surface
x3 - 2y2 + z4 = 5 at the point
P(1, -1, 1)

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