Consider the surface f(x,y,z)=x^2−y^2−4z^2+7=0, which may be regarded as a level surface of the function w=f(x,y,z). The point P(1,2,−1) is on the surface. a. Find the (three-dimensional) gradient...

Consider the surface

f(x,y,z)=x^2−y^2−4z^2+7=0,

which may be regarded as a level surface of the function

w=f(x,y,z).

The point

P(1,2,−1)

is on the surface.

a. Find the (three-dimensional) gradient of f and evaluate it at P.

b. The heads of all the vectors orthogonal to the gradient with their tails at P form a plane. Find an equation of that plane.

Jun 03, 2022

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