IDZ 10.1 - Option 29. Decisions Ryabushko AP

1. Find the domain of these functions.
1.29 z = 1 / (x2 + y2 - 6)

2. Find the partial derivatives and partial differentials of the following functions.
2.29 z = sin√y / (x + y)

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
3.29 f (x, y, z) = ze-xy, M0 (0, 1, 1)

4. Find the total differentials of these functions.
4.29 z = ey - x

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.
5.29 u = √x2 + y2 + 3, x = lnt, y = t3, 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.