Question

Find the angle of inclination θ of the tangent plane to the surface at the given point. (Round your answer to two decimal places.) 2xy−z 3=0,

Answer 1

To find the angle of inclination of the tangent plane to the surface, we need to calculate the gradient of the surface at the given point and then find the arctangent of the magnitude of the gradient.

Step-by-step explanation:

To find the angle of inclination θ of the tangent plane to the surface, we need to first find the gradient of the surface at the given point. The gradient of the surface is given by the partial derivatives with respect to x, y, and z.

Once we have the gradient, we can find the angle by taking the arctangent of the magnitude of the gradient.

Let's calculate it step by step:

1. Find the gradient of the surface by taking the partial derivatives.
2. Calculate the magnitude of the gradient.
3. Take the arctangent of the magnitude of the gradient to find the angle of inclination.