Exercises

Exercises for Lecture #3

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1-12. Find the higher-order partial derivatives of the functions:

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13-28. Find the total differentials of given functions

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

27. 28.

29-35. Using the Taylor’s formula

29. Expand in series of positive integral powers of h and k if .

Expand the following functions by Taylor’s formula in the neibourhood of the given point

30.

31.

32. Expand the following functions by Maclaurin’s series up to the terms of the third order inclusive:

.

33.Expand the following functions by Maclaurin’s series up to the terms of the four order inclusive:

.

34. Expand the following functions by Taylor’s formula in the neibourhood of the point (1,1) up to the terms of order two inclusive:

.

35. Expand the following functions by Taylor’s formula in the neibourhood of the point (1,-1) up to the terms of order three inclusive:

.