Questions to the colloquium on mathematical analysis for students of 1st year
(2009-2010 school year)
1. Theorem on the existence of the least upper bound.
2. The uniqueness of the limit of a convergent sequence. The limited convergent sequence.
3. Properties of limits sequences associated with inequalities.
4. Limit of the ratio of the two sequences.
5. Limit of a monotone sequence.
6. Cantor's theorem on the embedded intervals.
7. Theorem of Bolzano - Weierstrass existence of limit.
8. Cauchy criterion that the limit of the sequence
9. The equivalence of the two definitions of the limit functions
10. Limits of monotone functions.
11. Bounded continuous functions on the interval.
12. Attainability of the least upper (lower) bound on the interval of continuous
function.
13. The intermediate value theorem of continuous functions on the interval.
14. The inverse function theorem