Question

let S be the surface defined by x^4-2x^2y^2+3z^2=12, Find the equation of the tangent plane to the surface S at (0,1,2).

Answer #1

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 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 tangent plane to the surface
z=−3x2−1y2−2x+1y−1 at the point (4, 2,
-59).
z=________

Find an equation of the tangent plane to the surface z = x/y2 at
(−4, 2, −1).

Find an equation for the tangent plane to x^3+xy^2=3z at the
point(2,2,16/3)

1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) =
(2y − z, x − z, y + 3x). Use matrices to find the composition S ◦
T.
2. Find an equation of the tangent plane to the graph of x 2 − y
2 − 3z 2 = 5 at (6, 2, 3).
3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...

Let P be the plane given by the equation 2x + y − 3z = 2. The
point Q(1, 2, 3) is not on the plane P, the point R is on the plane
P, and the line L1 through Q and R is orthogonal to the plane P.
Let W be another point (1, 1, 3). Find parametric equations of the
line L2 that passes through points W and R.

Find equations of the tangent plane and normal line to the
surface x=2y^2+2z^2−159x at the point (1, -4, 8).
Tangent Plane: (make the coefficient of x equal to 1).
=0.
Normal line: 〈1,〈1, , 〉〉
+t〈1,+t〈1, ,

Find an equation of the tangent plane to the surface at the
given point. xy2 + 2x − z2 = 15, (4, −2, 3)

find the equation of the tangent plane to z= x^2y+2xy at
(1,5)

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