Question

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?

Answer #1

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

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

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

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.

Consider the function f(x,y)=y+sin(x/y)
a) Find the equation of the tangent plane to the graph offat the
point(1,3)
b) Find the linearization of the function f at the point(1;3)and
use it to approximate f(0:9;3:1).
c) Explain why f is differentiable at the point(1;3)
d)Find the differential of f
e) If (x,y) changes from (1,3) to (0.9,3.1), compare the values
of ‘change in f’ and df

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

Let f(x,y) = 9y^2 −(3x^2)y denote the temperature at the point
(x,y) in the plane, and let C(t) = (t^2, 3t) be the path of a
crawling ant in the plane. Find how fast the temperature of the ant
is changing at time t = 2.
At time t = 2 the ant is at the point C(2) = (4, 6). Which
direction should the ant crawl to warm up as quickly as possible
(in the near term)? Please a...

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).

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

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.

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