Find and sketch the domain of this function find all the

Question

1. Given f(x,y, z) = √(z- x² - y²)

(a. Find and sketch the domain of this function.

(b. Find all the first order partial derivatives of this function at (1, 1,3).

2. Suppose that xz -x In y = z². Find dz/dx and dz/dy at (1, 1, 0).

3. Given r^→(t) = e^2t sin ti^→ + 2j^→+ e^2t cos tk^→ with 0 ≤ t ≤ π.

(a) Find an equation of the tangent line to the curve at the point (0,2,1)

b. Find the length of this plan curve from (0, 2,1) to (e^π, 2, 0).