IDZ 10.1 - Option 9. Decisions Ryabushko AP

1. Find the domain of these functions.
1.9 z = √9-x2-y2

2. Find the partial derivatives and partial differentials of the following functions.
2.9 z = ln (3x2 - y4)

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
3.9 f (x, y, z) = arcsin (x2 / y - z), M0 (2, 5, 0)

4. Find the total differentials of these functions.
4.9 z = arcsin (x + y)

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.
5.9 u = x2e-y, x = sint, y = sin2t, 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.