[ Solutions to problems 1 2 3 4 5 6 7 | Lecture 4 | Home | Instructor ]

# Lecture 4: Exercises

• 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!