Question

- Find the tangent plane to the given surface of
*f(x,y)**=6-**6/**5**x-y*at the point (5, -1, 1). Make sure that your final answer for the plane is in simplified form.

Answer #1

f(x,y)=x^2+4xy-y^2 find an equation for the tangent
plane at the surface point (2,1,11)

We are given a level surface F ( x , y , z ) = 0 where F ( x , y
, z ) = x^3 - y^2 + z^4 - 20 . Find the equation of the tangent
plane to the surface at the point P ( 2 , 2 , 2 ) . Write the final
answer in the form a x + b y + c z + d = 0

Find an equation of the tangent plane to the given surface at
the specified point.
z = 2(x − 1)2 + 4(y + 3)2 +
1, (3, −1, 25)
Answer as z=

Find an equation of the tangent plane to the given parametric
surface at the specified point. x = u + v, y = 6u^2, z = u − v; (2,
6, 0)

Find an equation of the tangent plane to the given surface at
the specified point.
z = 2(x − 1)2 + 4(y + 3)2 +
9, (2, −2, 15)

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

(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 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 an equation of the tangent plane to the given surface at
the specified point. z = 8x^2 + y^2 − 7y, (1, 3, −4)

Find an equation of the tangent plane to the surface given
parametrically by x = u^2, y = v^2, z = u+4v at the point (1, 4,
9).

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