Question

Problem 1. Find an equation of the tangent plane to the given surface at the specified point. i) z = 2x 2 + y 2 − 5y, (1, 2, −4). ii) z = e x−y , (2, 2, 1). iii) z = x sin(x + y), (−1, 1, 0)

Answer #1

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=

Find an equation of the tangent plane to the given surface at
the specified point.
z = 2(x − 1)2 + 4(y + 3)2 +
9, (2, −2, 15)

Find an equation of the tangent plane to the given parametric
surface at the specified point. x = u + v, y = 6u^2, z = u − v; (2,
6, 0)

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 given surface at
the specified point.
z = 2x2 +
y2 −
7y, (1, 3, −10)

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

1)Find an equation of the tangent plane to the surface given by
the equation xy + e^2xz +3yz = −5, at the point, (0, −1, 2)
2)Find the local maximum and minimum values and saddle points
for the following function: f(x, y) = x − y+ 1 xy .
3)Use Lagrange multipliers to find the maximum and minimum
values of the function, f(x, y) = x^2 − y^2 subject to, x^2 + y 4 =
16.

Find an equation of the tangent plane to the surface given
parametrically by x = u^2, y = v^2, z = u+4v at the point (1, 4,
9).

Find the equation for tangent plane to the surface z=5e^yx^2 at
the point P(1,0,5)
Options Given:
1. z +10x - 5y = 5
2. z + 10x - 5y = -5
3. z - 10x - 5y = -5
4. z-10x - 5y = 5

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

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