IDZ 10.1 - Option 27. Decisions Ryabushko AP

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1. Find the domain of these functions.
1.27 z = √1-x-y

2. Find the partial derivatives and partial differentials of the following functions.
2.27 z = arcctgx3 / 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
3.27 f (x, y, z) = xz / (x - y), M0 (3, 1, 1)

4. Find the total differentials of these functions.
4.27 z = 2 - x3 - y3 + 5x

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.
5.27 u = ln (e2x + ey), x = t2, y = t4, 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.

Detailed solution. Decorated in Microsoft Word 2003. (Target decided to use formula editor)

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