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IDZ 10.1 - Option 17. Decisions Ryabushko AP

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  • 1. Find the domain of these functions.
  • 1.17 z = arccos (x + 2y)

  • 2. Find the partial derivatives and partial differentials of the following functions.
  • 2.17 z = ln (√xy-1)

  • 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
  • 3.17 f (x, y, z) = √zxy, M0 (1, 2, 4)

  • 4. Find the total differentials of these functions.
  • 4.17 z = xy4 - 3x2y + 1
  •  
  • 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.
  • 5.17 u = √x + y2 + 3, x = lnt, y = t2, 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.

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