Question

Find the equation for the level surface of the function f(x,y,z)=4x² +7y²−z² for the value c=1.

Answer 1

The equation for the level surface of the function f(x,y,z)=4x² +7y²−z² for c=1 is 4x² +7y² −z² = 1.

Step-by-step explanation:

To find the equation for the level surface of the function f(x,y,z)=4x² +7y²−z² for the value c=1, we set the function equal to 1 and get:

4x² +7y² −z² = 1.

This is the equation of the level surface at c=1. Each point (x, y, z) on this surface will satisfy the equation, representing a three-dimensional shape in space.