IDZ 10.1 - Option 4. Decisions Ryabushko AP

1. Find the domain of these functions.
1.4 z = ln (4 - x2 - y2)

2. Find the partial derivatives and partial differentials of the following functions.
2.4 z = cos (x3 - 2xy)

3. Calculate the value of partial f´x (M0), f´y (M0), f´z (M0), for the function f (x, y, z) at the point M0 (x0, y0, z0) with an accuracy of to two decimal places
3.4 f (x, y, z) = ln (x3 + 2y3 - z3), M0 (2, 1, 0)
 
4. Find the total differentials of these functions.
4.4 z = arcsin (xy) - 3xy2
 
5. Calculate the value of the derivative of a composite function u = u (x, y), where x = x (t), y = y (t), at t = t0 up to two decimal places.
5.4 u = ey - 2x + 2, x = sint, y = cost, t0 = π / 2

6. Calculate the values of the partial derivatives of the function z (x, y) given implicitly at the point M0 (x0, y0, z0) accurate to two decimal places.