The limsup and limit of the sequence n2 (meaning 1,4,9,16,...) are equal. T Ever

Question

The limsup and limit of the sequence n2 (meaning 1,4,9,16,...) are equal. T Every bounded sequence has at most one convergent subsequence. Are the following characteristic functions Riemann integrable on the interval [0, 1]? (yes, no, yes, no, no) No continuous function f: R rightarrow R can have a minimum value. (False) Let I1 I2 I3 be a nested sequence of closed intervals in R whose lengths form a sequence converging to 0. choose points an I for each n. Then the sequence am converges. (I think it's true) Consider a function f: R rightarrow R. Which of the following statements are true? (yes, no yes, no, yes, yes) If f is continuous, then it maps every compact set onto a compact set? If f maps every compact set onto a compact set, then it is continuous. If f is continuous, then it maps every connected set onto a connected set? Is it true that if f maps every connected set onto a connected set, then it is continuous. Is it true that if f is continuous, then it maps every open set onto an open set? If maps every open set onto an open set, then it is continuous. 0. Choose

Explanation / Answer

1. True 2. False 3. yes, no, yes, no, no 4. False 5. True 6. yes, no, yes, no, yes, yes

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