Question

An implicitly defined function of x, y and z is given along with a point P that lies on the surface: sin(xy) + cos(yz) = 0, at P = (2, π/12, 4)

Use the gradient ∇F to:

(a) find the equation of the normal line to the surface at P.

(b) find the equation of the plane tangent to the surface at P.

Answer #1

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).

Consider the surface S in R3 defined implicitly by x**2 y =
4ze**(x+y) − 35 .
(a) Find the equations of the implicit partial derivatives ∂z ∂x
and ∂z ∂y in terms of x, y, z. (b) Find equations of the tangent
plane and the norma line to the surface S at the point (3, −3,
2)

Suppose z is implicitly implicitly defined by the equation:
F(x, y, z) = 4x^ −1 − 3x 3 yz + e^ z/ (x − 2) = c where c is a
constant.
Compute the first and second order partial derivatives of z with
respect to x and y

(1 point) If the gradient of f is ∇f=z3j⃗ −2yi⃗ −xzk⃗ and the
point P=(10,−7,−4) lies on the level surface f(x,y,z)=0, find an
equation for the tangent plane to the surface at the point P.
z=

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

Given the level surface S defined by f(x, y, z) = x −
y3 − 2z2 = 2 and the point P0(−4,
−2, 1).
Find the equation of the tangent plane to the surface S at the
point P0.
Find the derivative of f at P0in the direction of
r(t) =< 3, 6, −2 >
Find the direction and the value of the maximum rate of change
greatest increase of f at P0;
(d) Find the parametric equations of the...

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

Compute equations of tangent plane and normal line to the
surface z = x cos (x+y) at point (π/2, π/3, -√3π/4).

Find the tangent plane to the surface z = cos(xy) when (x, y) =
(π, 0).

Identify the surface with parametrization x = 3 cos θ sin φ, y =
3 sin θ sin φ, z = cos φ where 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π. Hint: Find
an equation of the form F(x, y, z) = 0 for this surface by
eliminating θ and φ from the equations above. (b) Calculate a
parametrization for the tangent plane to the surface at (θ, φ) =
(π/3, π/4).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 19 minutes ago

asked 28 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago