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# Lecture 4: Exercises

### Suggestions for further reading

- Differentiation: Bronstein&Semendjajew (chaps. 3.1.5, 3.1.6)
- Integration: Bronstein&Semendjajew (chap. 3.1.7), Lyons (appendix A4)

### Questions for Review

- Remember the derivatives of the following elementary functions:
- x^n, 1/x and 1/x^n
- n-th root of x
- exp(x)
- ln(x)
- sin(x), cos(x), tan(x) and cot(x)
- arcsin(x), arccos(x), arctan(x) and arccot(x)

- What is a local extremum?
How are local extrema of a differentiable function characterized?
- If f'(x)=0 at some x, what can you conclude about the behavior
of the function f at that point?
How can you obtain additional information?
- What can you say about the second derivative at a local maximum
or minimum, respectively?
- What is a partial derivative?
- What is an indefinite integral? Is it unique?
- What is a definite integral? How can it be visualized?
- How are indefinite and definite integrals related?
- What are the principal methods for evaluating integrals? Explain!

### Problems