Exercises

Exercises for Lectures #10

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1. Find , if

2. Prove that the function satisfies the Laplace equation

3. The Laplace transformation F(p) for the function f(t) is defined by the formula

Find F(p), if: a) f(t)=1; b); c); d) .

Evaluate the following improper integrals:

4.

5.

6. , where S is a region defined by the inequalities .

7. *

Applying differentiation with respect to a parameter, evaluate the following integrals:

8. .

9. .

10.