Question Number 31674 by gunawan last updated on 12/Mar/18
$$\mathrm{let}\:\mathrm{p}_{{n}} \left({x}\right)\:\mathrm{polinom}\:\mathrm{Maclaurin}\:\mathrm{for} \\ $$$$\mathrm{function}\:{f}\left({x}\right)={e}^{{x}} .\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{degree}\:\mathrm{minimal}\:\mathrm{polinom}\:\left({n}\right)\:\mathrm{so} \\ $$$$\mid{e}^{{x}} −\mathrm{p}_{{n}} \left({x}\right)\mid\leqslant\:\mathrm{10}^{−\mathrm{2}} ,\:\mathrm{for}\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}? \\ $$