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Author: Tinku Tara

1-lim-n-6-6-6-6-1-3-1-3-1-3-1-3-

Question Number 143327 by SOMEDAVONG last updated on 13/Jun/21 $$\mathrm{1}/.\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{6}+\sqrt[{\mathrm{3}}]{\mathrm{6}+\sqrt[{\mathrm{3}}]{\mathrm{6}+……….+\sqrt[{\mathrm{3}}]{\mathrm{6}}}}}=? \\ $$ Answered by MJS_new last updated on 13/Jun/21 $${y}=\sqrt[{\mathrm{3}}]{\mathrm{6}+\sqrt[{\mathrm{3}}]{\mathrm{6}+…}} \\ $$$${y}^{\mathrm{3}} =\mathrm{6}+{y} \\…

L-lim-n-2-3-1-3-3-1-4-3-1-n-3-1-2-3-1-3-3-1-4-3-1-n-3-1-

Question Number 143326 by SOMEDAVONG last updated on 13/Jun/21 $$\mathrm{L}=\:\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\frac{\left(\mathrm{2}^{\mathrm{3}} −\mathrm{1}\right)\left(\mathrm{3}^{\mathrm{3}} −\mathrm{1}\right)\left(\mathrm{4}^{\mathrm{3}} −\mathrm{1}\right)…\left(\mathrm{n}^{\mathrm{3}} −\mathrm{1}\right)}{\left(\mathrm{2}^{\mathrm{3}} +\mathrm{1}\right)\left(\mathrm{3}^{\mathrm{3}} +\mathrm{1}\right)\left(\mathrm{4}^{\mathrm{3}} +\mathrm{1}\right)…\left(\mathrm{n}^{\mathrm{3}} +\mathrm{1}\right)} \\ $$ Answered by gsk2684 last…

Let-g-x-be-an-ininitely-differentiable-function-such-that-g-2x-6-g-3x-1-for-all-x-given-that-g-44-3-33-find-g-8-

Question Number 12246 by tawa last updated on 16/Apr/17 $$\mathrm{Let}\:\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{an}\:\mathrm{ininitely}\:\mathrm{differentiable}\:\mathrm{function}\:,\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{g}\left(\mathrm{2x}\:+\:\mathrm{6}\right)\:=\:\mathrm{g}^{'} \left(\mathrm{3x}\:−\:\mathrm{1}\right)\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}. \\ $$$$\mathrm{given}\:\mathrm{that}\:\:\mathrm{g}\left(\frac{\mathrm{44}}{\mathrm{3}}\right)\:=\:\mathrm{33}\:.\:\:\mathrm{find}\:\:\:\mathrm{g}''\left(\mathrm{8}\right) \\ $$ Answered by mrW1 last updated on 16/Apr/17 $${u}=\mathrm{3}{x}−\mathrm{1}\Rightarrow{x}=\frac{{u}+\mathrm{1}}{\mathrm{3}}\Rightarrow\mathrm{2}{x}+\mathrm{6}=\mathrm{2}×\frac{{u}+\mathrm{1}}{\mathrm{3}}+\mathrm{6}=\frac{\mathrm{2}{u}+\mathrm{20}}{\mathrm{3}}…

Solve-the-differential-equation-dy-dx-4x-2y-3-8x-4y-5-

Question Number 12245 by tawa last updated on 16/Apr/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{4x}\:+\:\mathrm{2y}\:−\:\mathrm{3}}{\mathrm{8x}\:−\:\mathrm{4y}\:+\:\mathrm{5}} \\ $$ Answered by mrW1 last updated on 17/Apr/17 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{4x}\:+\:\mathrm{2y}\:−\:\mathrm{3}}{\mathrm{8x}\:−\:\mathrm{4y}\:+\:\mathrm{5}} \\ $$$$ \\…

0-sin-4-x-x-4-dx-pi-3-

Question Number 143312 by Ar Brandon last updated on 12/Jun/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{4}} \mathrm{x}}{\mathrm{x}^{\mathrm{4}} }\mathrm{dx}=\frac{\pi}{\mathrm{3}} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\mathrm{1}\:\left(\mathrm{constant}\:\mathrm{function}\:\mathrm{unity}\right)…