求sin(cosA)的极值

王守恩

王守恩 发表于 2018-1-31 14:12
感谢高手们的帮助！这样说可以吗？

\(\D\frac{\frac{(\frac{1}{1})^0}{0!}+\frac{(\frac{1}{1})^2}{2! ...

感谢高手们的帮助！这样说也可以。

\(\D\frac{\frac{(\frac{2}{1})^1}{1!}+\frac{(\frac{2}{1})^5}{5!}+\frac{(\frac{2}{1})^9}{9!}+\frac{(\frac{2}{1})^{13}}{13!}+\frac{(\frac{2}{1})^{17}}{17!}+......}{\frac{(\frac{2}{1})^2}{2!}+\frac{(\frac{2}{1})^6}{6!}+\frac{(\frac{2}{1})^{10}}{10!}+\frac{(\frac{2}{1})^{14}}{14!}+\frac{(\frac{2}{1})^{18}}{18!}+......}⟹1\)

\(\D\frac{\frac{(\frac{2}{2})^1}{1!}+\frac{(\frac{2}{2})^5}{5!}+\frac{(\frac{2}{2})^9}{9!}+\frac{(\frac{2}{2})^{13}}{13!}+\frac{(\frac{2}{2})^{17}}{17!}+......}{\frac{(\frac{2}{2})^2}{2!}+\frac{(\frac{2}{2})^6}{6!}+\frac{(\frac{2}{2})^{10}}{10!}+\frac{(\frac{2}{2})^{14}}{14!}+\frac{(\frac{2}{2})^{18}}{18!}+......}⟹2\)

\(\D\frac{\frac{(\frac{2}{3})^1}{1!}+\frac{(\frac{2}{3})^5}{5!}+\frac{(\frac{2}{3})^9}{9!}+\frac{(\frac{2}{3})^{13}}{13!}+\frac{(\frac{2}{3})^{17}}{17!}+......}{\frac{(\frac{2}{3})^2}{2!}+\frac{(\frac{2}{3})^6}{6!}+\frac{(\frac{2}{3})^{10}}{10!}+\frac{(\frac{2}{3})^{14}}{14!}+\frac{(\frac{2}{3})^{18}}{18!}+......}⟹3\)

\(\D\frac{\frac{(\frac{2}{4})^1}{1!}+\frac{(\frac{2}{4})^5}{5!}+\frac{(\frac{2}{4})^9}{9!}+\frac{(\frac{2}{4})^{13}}{13!}+\frac{(\frac{2}{4})^{17}}{17!}+......}{\frac{(\frac{2}{4})^2}{2!}+\frac{(\frac{2}{4})^6}{6!}+\frac{(\frac{2}{4})^{10}}{10!}+\frac{(\frac{2}{4})^{14}}{14!}+\frac{(\frac{2}{4})^{18}}{18!}+......}⟹4\)

\(\D\frac{\frac{(\frac{2}{5})^1}{1!}+\frac{(\frac{2}{5})^5}{5!}+\frac{(\frac{2}{5})^9}{9!}+\frac{(\frac{2}{5})^{13}}{13!}+\frac{(\frac{2}{5})^{17}}{17!}+......}{\frac{(\frac{2}{5})^2}{2!}+\frac{(\frac{2}{5})^6}{6!}+\frac{(\frac{2}{5})^{10}}{10!}+\frac{(\frac{2}{5})^{14}}{14!}+\frac{(\frac{2}{5})^{18}}{18!}+......}⟹5\)

\(\D\frac{\frac{(\frac{2}{6})^1}{1!}+\frac{(\frac{2}{6})^5}{5!}+\frac{(\frac{2}{6})^9}{9!}+\frac{(\frac{2}{6})^{13}}{13!}+\frac{(\frac{2}{6})^{17}}{17!}+......}{\frac{(\frac{2}{6})^2}{2!}+\frac{(\frac{2}{6})^6}{6!}+\frac{(\frac{2}{6})^{10}}{10!}+\frac{(\frac{2}{6})^{14}}{14!}+\frac{(\frac{2}{6})^{18}}{18!}+......}⟹6\)

\(\D\frac{\frac{(\frac{2}{7})^1}{1!}+\frac{(\frac{2}{7})^5}{5!}+\frac{(\frac{2}{7})^9}{9!}+\frac{(\frac{2}{7})^{13}}{13!}+\frac{(\frac{2}{7})^{17}}{17!}+......}{\frac{(\frac{2}{7})^2}{2!}+\frac{(\frac{2}{7})^6}{6!}+\frac{(\frac{2}{7})^{10}}{10!}+\frac{(\frac{2}{7})^{14}}{14!}+\frac{(\frac{2}{7})^{18}}{18!}+......}⟹7\)

\(\D\frac{\frac{(\frac{2}{8})^1}{1!}+\frac{(\frac{2}{8})^5}{5!}+\frac{(\frac{2}{8})^9}{9!}+\frac{(\frac{2}{8})^{13}}{13!}+\frac{(\frac{2}{8})^{17}}{17!}+......}{\frac{(\frac{2}{8})^2}{2!}+\frac{(\frac{2}{8})^6}{6!}+\frac{(\frac{2}{8})^{10}}{10!}+\frac{(\frac{2}{8})^{14}}{14!}+\frac{(\frac{2}{8})^{18}}{18!}+......}⟹8\)

\(\D\frac{\frac{(\frac{2}{9})^1}{1!}+\frac{(\frac{2}{9})^5}{5!}+\frac{(\frac{2}{9})^9}{9!}+\frac{(\frac{2}{9})^{13}}{13!}+\frac{(\frac{2}{9})^{17}}{17!}+......}{\frac{(\frac{2}{9})^2}{2!}+\frac{(\frac{2}{9})^6}{6!}+\frac{(\frac{2}{9})^{10}}{10!}+\frac{(\frac{2}{9})^{14}}{14!}+\frac{(\frac{2}{9})^{18}}{18!}+......}⟹9\)

王守恩

王守恩 发表于 2018-2-1 15:07
感谢高手们的帮助！这样说也可以。

\(\D\frac{\frac{(\frac{2}{1})^1}{1!}+\frac{(\frac{2}{1})^5}{5! ...

感谢高手们的帮助！这样说还是可以。

\(\D\frac{\frac{(\frac{2}{1})^{0}}{0!}+\frac{(\frac{2}{1})^{2}}{4!}+\frac{(\frac{2}{1})^{4}}{8!}+\frac{(\frac{2}{1})^{6}}{12!}+\frac{(\frac{2}{1})^{8}}{16!}+......}{\frac{(\frac{2}{1})^{1}}{2!}+\frac{(\frac{2}{1})^{3}}{6!}+\frac{(\frac{2}{1})^{5}}{10!}+\frac{(\frac{2}{1})^{7}}{14!}+\frac{(\frac{2}{1})^{9}}{18!}+......}⟹1\)

\(\D\frac{\frac{(\frac{2}{2})^{0}}{0!}+\frac{(\frac{2}{2})^{2}}{4!}+\frac{(\frac{2}{2})^{4}}{8!}+\frac{(\frac{2}{2})^{6}}{12!}+\frac{(\frac{2}{2})^{8}}{16!}+......}{\frac{(\frac{2}{2})^{1}}{2!}+\frac{(\frac{2}{2})^{3}}{6!}+\frac{(\frac{2}{2})^{5}}{10!}+\frac{(\frac{2}{2})^{7}}{14!}+\frac{(\frac{2}{2})^{9}}{18!}+......}⟹2\)

\(\D\frac{\frac{(\frac{2}{3})^{0}}{0!}+\frac{(\frac{2}{3})^{2}}{4!}+\frac{(\frac{2}{3})^{4}}{8!}+\frac{(\frac{2}{3})^{6}}{12!}+\frac{(\frac{2}{3})^{8}}{16!}+......}{\frac{(\frac{2}{3})^{1}}{2!}+\frac{(\frac{2}{3})^{3}}{6!}+\frac{(\frac{2}{3})^{5}}{10!}+\frac{(\frac{2}{3})^{7}}{14!}+\frac{(\frac{2}{3})^{9}}{18!}+......}⟹3\)

\(\D\frac{\frac{(\frac{2}{4})^{0}}{0!}+\frac{(\frac{2}{4})^{2}}{4!}+\frac{(\frac{2}{4})^{4}}{8!}+\frac{(\frac{2}{4})^{6}}{12!}+\frac{(\frac{2}{4})^{8}}{16!}+......}{\frac{(\frac{2}{4})^{1}}{2!}+\frac{(\frac{2}{4})^{3}}{6!}+\frac{(\frac{2}{4})^{5}}{10!}+\frac{(\frac{2}{4})^{7}}{14!}+\frac{(\frac{2}{4})^{9}}{18!}+......}⟹4\)

\(\D\frac{\frac{(\frac{2}{5})^{0}}{0!}+\frac{(\frac{2}{5})^{2}}{4!}+\frac{(\frac{2}{5})^{4}}{8!}+\frac{(\frac{2}{5})^{6}}{12!}+\frac{(\frac{2}{5})^{8}}{16!}+......}{\frac{(\frac{2}{5})^{1}}{2!}+\frac{(\frac{2}{5})^{3}}{6!}+\frac{(\frac{2}{5})^{5}}{10!}+\frac{(\frac{2}{5})^{7}}{14!}+\frac{(\frac{2}{5})^{9}}{18!}+......}⟹5\)

\(\D\frac{\frac{(\frac{2}{6})^{0}}{0!}+\frac{(\frac{2}{6})^{2}}{4!}+\frac{(\frac{2}{6})^{4}}{8!}+\frac{(\frac{2}{6})^{6}}{12!}+\frac{(\frac{2}{6})^{8}}{16!}+......}{\frac{(\frac{2}{6})^{1}}{2!}+\frac{(\frac{2}{6})^{3}}{6!}+\frac{(\frac{2}{6})^{5}}{10!}+\frac{(\frac{2}{6})^{7}}{14!}+\frac{(\frac{2}{6})^{9}}{18!}+......}⟹6\)

\(\D\frac{\frac{(\frac{2}{7})^{0}}{0!}+\frac{(\frac{2}{7})^{2}}{4!}+\frac{(\frac{2}{7})^{4}}{8!}+\frac{(\frac{2}{7})^{6}}{12!}+\frac{(\frac{2}{7})^{8}}{16!}+......}{\frac{(\frac{2}{7})^{1}}{2!}+\frac{(\frac{2}{7})^{3}}{6!}+\frac{(\frac{2}{7})^{5}}{10!}+\frac{(\frac{2}{7})^{7}}{14!}+\frac{(\frac{2}{7})^{9}}{18!}+......}⟹7\)

\(\D\frac{\frac{(\frac{2}{8})^{0}}{0!}+\frac{(\frac{2}{8})^{2}}{4!}+\frac{(\frac{2}{8})^{4}}{8!}+\frac{(\frac{2}{8})^{6}}{12!}+\frac{(\frac{2}{8})^{8}}{16!}+......}{\frac{(\frac{2}{8})^{1}}{2!}+\frac{(\frac{2}{8})^{3}}{6!}+\frac{(\frac{2}{8})^{5}}{10!}+\frac{(\frac{2}{8})^{7}}{14!}+\frac{(\frac{2}{8})^{9}}{18!}+......}⟹8\)

\(\D\frac{\frac{(\frac{2}{9})^{0}}{0!}+\frac{(\frac{2}{9})^{2}}{4!}+\frac{(\frac{2}{9})^{4}}{8!}+\frac{(\frac{2}{9})^{6}}{12!}+\frac{(\frac{2}{9})^{8}}{16!}+......}{\frac{(\frac{2}{9})^{1}}{2!}+\frac{(\frac{2}{9})^{3}}{6!}+\frac{(\frac{2}{9})^{5}}{10!}+\frac{(\frac{2}{9})^{7}}{14!}+\frac{(\frac{2}{9})^{9}}{18!}+......}⟹9\)