Question

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

Answer #1

Find the equations of (i) the tangent plane and (ii) the normal
line to the surface 2(x − 2)^2 + (y − 1)^2 + (z − 3)^2 = 10, at the
point (3, 3, 5)

Find equations of the tangent plane and normal line to the
surface z+2=xeycosz at the point (2, 0, 0).

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

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 equations of the tangent plane and normal line to the
surface x=3y^2+1z^2−40x at the point (-9, 3, 2).
Tangent Plane: (make the coefficient of x equal to 1).
=0.
Normal line: 〈−9,〈−9, , 〉〉
+t〈1,+t〈1, , 〉〉.

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).

Find equations of the tangent plane and normal line to the
surface
?=1?2+4?2−321x=1y2+4z2−321
at the point (7, 2, 9).
Tangent Plane: (make the coefficient of x equal to 1).

Find an equation of the tangent plane and find the equations for
the normal line to
the following surface at the given point.
3xyz = 18 at (1, 2, 3)

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

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.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 8 minutes ago

asked 20 minutes ago

asked 31 minutes ago

asked 52 minutes 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 2 hours ago