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1. Some convergent sequences and their limits are given. Find the order of convergence for each. (a) $?n_{n}n!???0$ (b) $?3_{e_{n}}1???0_{[5}$ (c) $?2_{2_{n}}+32_{2_{n}}?2???1_{[[s]}$ (d) $?1+n_{2}n_{2}???1_{[A]}$ (e) $?f_{?n}(1)??3?$ where $f(x)=2xx_{2}+3?$. Note: $f_{?n}$ means $f$ composed with itself $n$ times.

(a) The order of convergence for the sequence \langle(n!)/(n ^ n)\rangle -> 0 is super-exponential.(b) The ord