Question

Find the equation of the tangent plane to the surface z=e^(−2x/17)ln(3y) at the point (−2,4,3.1441).

Answer #1

Find an equation of the tangent plane to the given surface at
the specified point.
z = 3x2 - y2 +
3y, (-3, 3, 27)

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

Find the equation of the tangent plane to the surface given by z =
ln (2tan x - tan y) at (pi/4, pi/4, 0).

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

Find an equation of the tangent plane to the given surface at
the specified point.
z = 2x2 +
y2 −
7y, (1, 3, −10)

(a) Find an equation of the plane tangent to the surface xy ln x
− y^2 + z^2 + 5 = 0 at the point (1, −3, 2)
(b) Find the directional derivative of f(x, y, z) = xy ln x −
y^2 + z^2 + 5 at the point (1, −3, 2) in the direction of the
vector < 1, 0, −1 >. (Hint: Use the results of partial
derivatives from part(a))

Find an equation of the tangent plane to the given surface at
the specified point. z = 8x^2 + y^2 − 7y, (1, 3, −4)

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

Find an equation of the tangent plane to the given surface at
the specified point.
z = 2(x − 1)2 + 4(y + 3)2 +
1, (3, −1, 25)
Answer as z=

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