# IDZ 10.1 - Option 19. Decisions Ryabushko AP

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Content: 19v-IDZ10.1.doc 132,5 kB

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1. Find the domain of these functions.
1.19 z = ln (9 - x2 - y2)

2. Find the partial derivatives and partial differentials of the following functions.
2.19 z = arctg (x2 / y3)

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
3.19 f (x, y, z) = ln (x3 + 3√y - z), M0 (2, 1, 8)

4. Find the total differentials of these functions.
4.19 z = 2x2y2 + x3 - y3

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.
5.19 u = y2 / x, x = 1-2t, y = 1 + arctgt, t0 = 0

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.