IDZ 10.1 - Option 17. Decisions Ryabushko AP

1. Find the domain of these functions.
1.17 z = arccos (x + 2y)

2. Find the partial derivatives and partial differentials of the following functions.
2.17 z = ln (√xy-1)

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
3.17 f (x, y, z) = √zxy, M0 (1, 2, 4)

4. Find the total differentials of these functions.
4.17 z = xy4 - 3x2y + 1
 
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.
5.17 u = √x + y2 + 3, x = lnt, y = t2, t0 = 1

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.