Question

Determine a equation tangent to the plane f(x,y)=x^2+y^3 at (3,1) and then calculate and classify the critical points of minor x.

Answer #1

LET F(x,y) = ycos(x-y) . Determine the equation of the tangent
plane to F at point (2,2,2). Then, determine the linear
approximation of F near (2,2). How can you justify that this is
correct?

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

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

1. Find the equation of the tangent plane to the function f ( x,
y ) = x^2 + y^2 at the point (1,1).
2. Find a different solution to Laplace's equation.

Let f(x, y) = x tan(xy^2) + ln(2y). Find the equation of the
tangent plane at (π, 1⁄2).

Find an equation of the tangent plane to z=32-3(x^2)-4(y^2) at
the point (2,1,16)

(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))

Let f(x,y)=3xy−5x2−2y2
Then an equation for the tangent plane to the graph of ff at the
point (3,3)(3,3) is

Find the equation of the tangent plane (in terms of x, y and z)
to the surface given by x = u, y = v and z = uv at the point (3, 2,
6).

for w=f(x,y,z)=2x^4y^2-6xz^3 use the tangent plane to
estimate f(-2.03,1.04,1.02)

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