Question

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

Answer #1

Equation of tangent plane:

first do partial derivative with respect to x,y and z and substitute point in that derivative.

Now form equation of tangent plane with these using formula.

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 = 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 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)

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

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)

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 surface z = x^2 +
xy + 3y^2 at the point (1, 1, 5)

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).

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