Question Number 153598 by liberty last updated on 08/Sep/21
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}cos}\:\left({n}\pi\:\sqrt[{\mathrm{2}{n}}]{{e}}\:\right)=? \\ $$
Commented by tabata last updated on 08/Sep/21
$$\boldsymbol{{y}}=\:\boldsymbol{{n}\pi}\:\sqrt[{\mathrm{2}\boldsymbol{{n}}}]{\boldsymbol{{e}}}\: \\ $$$$ \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{y}}\rightarrow\infty} \:\boldsymbol{{cos}}\left(\boldsymbol{{y}}\right)\:=\:\infty \\ $$$$ \\ $$$$\langle\:\boldsymbol{{M}}\:.\:\boldsymbol{{T}}\:\:\rangle \\ $$
Commented by MJS_new last updated on 08/Sep/21
$$−\mathrm{1}\leqslant\mathrm{cos}\:{y}\:\leqslant\mathrm{1}\:\forall\:{y}\in\mathbb{R}\:\Rightarrow\:\mathrm{the}\:\mathrm{limit}\:\mathrm{cannot}\:\mathrm{be}\:+\infty \\ $$
Commented by bramlexs22 last updated on 09/Sep/21
$$\mathrm{answer}\:\mathrm{is}\:\mathrm{zero} \\ $$