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Consider the surface with parametric equations. a) Find the equation of the tangent plane at...

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Final answer:

The equation of the tangent plane at a point on a surface with parametric equations can be found using the partial derivatives of the equations.

Step-by-step explanation:

The equation of the tangent plane at a point on a surface with parametric equations can be found using the partial derivatives of the equations. Let's say the surface is defined by the parametric equations x = f(u, v), y = g(u, v), and z = h(u, v). To find the equation of the tangent plane at a point (u0, v0), we can use the following formula:

z - h(u0, v0) = (dz/du)(u - u0) + (dz/dv)(v - v0)

Here, (dz/du) and (dz/dv) are the partial derivatives of z with respect to u and v, evaluated at (u0, v0).

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