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### Questions (18)

 6 $\displaystyle\lim_{n\to \infty} n^2(\sqrt[n]{2}-\sqrt[n+1]{2})$ 5 Infimum, supremum of a set problems 5 How many functions $f:\{1,2,3,4\}→\{1,2,3,4\}$ satisfy $f(1)=f(4)$? 3 Limit of sequence, sequence is formed by the root of an equation. 3 Largest element of the set $\{ \sin{1}, \sin{2}, \sin{3}\}$

### Reputation (217)

 +10 How many functions $f:\{1,2,3,4\}→\{1,2,3,4\}$ satisfy $f(1)=f(4)$? +5 How many functions $f: \{1, 2, 3, \dots, 10\} \to \{0,1\}$ satisfy $f(1) + f(2) + \dots + f(10) = 2$? +5 $\displaystyle\lim_{n\to \infty} n^2(\sqrt[n]{2}-\sqrt[n+1]{2})$ +5 Applying the Cesaro-Stolz Theorem recursively

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### Tags (14)

 0 algebra-precalculus × 10 0 absolute-value × 3 0 calculus × 7 0 arithmetic × 2 0 real-analysis × 6 0 combinatorics × 2 0 sequences-and-series × 4 0 fractions × 2 0 trigonometry × 3 0 functions × 2

### Account (1)

 Mathematics 217 rep 17