Question

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, , 〉〉.

Answer #1

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

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 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)

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 an equation of the tangent plane to the surface z = x^2 +
xy + 3y^2 at the point (1, 1, 5)

A) Find the equations of the tangent plane and normal line to
the graph of f(x, y) =(x/1+x2y) (1, 2).
B)Evaluate the limit or explain why it does not exist .
lim(x,y)→(0,0)
(2x2+5y)2/x4+4y2

Find an equation of the tangent plane to the surface
z=1x^2+1y^2+1x+3y−3 at the point (4, 1, 21).

Find the point on the surface z = x 2 + 2y 2 where the tangent
plane is orthogonal to the line connecting the points (3, 0, 1) and
(1, 4, 0).

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