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Author: Tinku Tara

expand-y-e-x-about-the-point-x-1-using-taylor-s-series-

Question Number 9400 by tawakalitu last updated on 04/Dec/16 $$\mathrm{expand}\::\:\:\mathrm{y}\:=\:\mathrm{e}^{\mathrm{x}} \:,\:\mathrm{about}\:\mathrm{the}\:\mathrm{point}\:\mathrm{x}\:=\:\mathrm{1} \\ $$$$\mathrm{using}\:\mathrm{taylor}'\mathrm{s}\:\mathrm{series}. \\ $$ Answered by 123456 last updated on 04/Dec/16 $${y}=\frac{{dy}}{{dx}}=…\:\mathrm{for}\:{y}={e}^{{x}} \\ $$$$\mathrm{taylor}\:\mathrm{serie}…

a-b-c-R-x-1-ax-4-bx-2-c-1-x-2-1-proof-a-16-

Question Number 140468 by mathdanisur last updated on 08/May/21 $${a};{b};{c}\in\mathbb{R}\:;\:\forall\mid{x}\mid\leqslant\mathrm{1} \\ $$$$\mid{ax}^{\mathrm{4}} +{bx}^{\mathrm{2}} +{c}\mid\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\leqslant\mathrm{1}\:;\:{proof}\:\mid{a}\mid\leqslant\mathrm{16} \\ $$ Commented by mathdanisur last updated on 11/May/21 $${Sir},\:{mr}.{W}\:{my}\:{dear}\:{friend}\:{please}……

If-lim-x-0-cos-x-a-sin-bx-1-x-e-2-a-b-

Question Number 140471 by EDWIN88 last updated on 08/May/21 $$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{a}\:\mathrm{sin}\:\mathrm{bx}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \:=\:\mathrm{e}^{\mathrm{2}} \\ $$$$\:\begin{cases}{\mathrm{a}=?}\\{\mathrm{b}=?}\end{cases} \\ $$ Answered by benjo_mathlover last updated on 08/May/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}\:\mathrm{x}+\:\mathrm{a}\:\mathrm{sin}\:\mathrm{bx}\right)^{\frac{\mathrm{1}}{\mathrm{x}}}…

f-x-2-f-1-x-1-x-64x-x-D-f-x-

Question Number 140470 by EDWIN88 last updated on 08/May/21 $$\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} .\:\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\:=\:\mathrm{64x}\:,\:\forall\mathrm{x}\in\mathrm{D} \\ $$$$\Rightarrow\:\mathrm{f}\left(\mathrm{x}\right)\:=? \\ $$ Answered by benjo_mathlover last updated on 08/May/21 $$\left(\mathrm{1}\right)\:\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} .\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\:=\:\mathrm{64x} \\…