IDZ 10.1 - Option 18. Decisions Ryabushko AP

1. Find the domain of these functions.
1.18 z = arcsin (2x - y)

2. Find the partial derivatives and partial differentials of the following functions.
2.18 z = arcsin (2x3y)

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
3.18 f (x, y, z) = -z / √x2 + y2, M0 (√2, √2, √2)

4. Find the total differentials of these functions.
4.18 z = ln (x + xy - y2)
 
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.
5.18 u = arcsin (x2 / y), x = sint, y = cost, t0 = π

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.