 # IDZ 10.1 - Option 5. Decisions Ryabushko AP

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1. Find the domain of these functions.
1.5 z = 2 / (6 - x2 - y2)

2. Find the partial derivatives and partial differentials of the following functions.
2.5 z = sin√y / x3

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
3.5 f (x, y, z) = x / √y2 + z2, M0 (1, 0, 1)

4. Find the total differentials of these functions.
4.5 z = 5xy4 + 2x2y7

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.
5.5 u = x2ey, x = cost, y = sint, 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. 