IDZ 10.1 - Option 6. Decisions Ryabushko AP

IDZ 10.1 - Option 6. Decisions Ryabushko AP

1. Find the domain of these functions.
1.6 z = √x2 + y2-5

2. Find the partial derivatives and partial differentials of the following functions.
2.6 z = tg (x3 + y2)
 
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
3.6 f (x, y, z) = lncos (x2y2 + z), M0 (0, 0, π / 4)

4. Find the total differentials of these functions.
4.6 z = cos (x2 - y2) + x3

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.
5.6 u = ln (ex + ey), x = t2, 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.

Additional information:

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