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Author: Tinku Tara

f-N-R-g-N-R-f-n-0-2pi-x-n-sin-xdx-g-n-0-2pi-x-n-cos-xdx-f-n-1-f-n-g-n-1-g-n-

Question Number 949 by 123456 last updated on 04/May/15 $${f}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{N}\rightarrow\mathbb{R} \\ $$$${f}\left({n}\right)=\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}{x}^{{n}} \mathrm{sin}\:{xdx} \\ $$$${g}\left({n}\right)=\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}{x}^{{n}} \mathrm{cos}\:{xdx} \\ $$$$\frac{{f}\left({n}+\mathrm{1}\right)−{f}\left({n}\right)}{{g}\left({n}+\mathrm{1}\right)−{g}\left({n}\right)}=? \\…

Trigonometry-What-is-the-minimum-value-of-3sin-x-4cos-x-10-3sin-x-4cos-x-10-

Question Number 132016 by bramlexs22 last updated on 10/Feb/21 $$\mathrm{Trigonometry} \\ $$$$\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\sqrt{\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{4cos}\:\mathrm{x}−\mathrm{10}\right)\left(\mathrm{3sin}\:\mathrm{x}+\mathrm{4cos}\:\mathrm{x}−\mathrm{10}\right)}\:. \\ $$ Answered by EDWIN88 last updated on 11/Feb/21 $$\:\mathrm{consider}\:\left(\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{10}\right)−\mathrm{4cos}\:\mathrm{x}\right)\left(\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{10}\right)+\mathrm{4cos}\:\mathrm{x}\right)= \\…

lim-x-2-log-x-2-1-log-2-1-x-1-

Question Number 66478 by hmamarques1994@gmail.com last updated on 15/Aug/19 $$\: \\ $$$$\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{2}} {\boldsymbol{{lim}}}\left[\frac{\boldsymbol{{log}}_{\boldsymbol{{x}}} \left(\mathrm{2}\right)−\mathrm{1}}{\boldsymbol{{log}}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\boldsymbol{{x}}}\right)+\mathrm{1}}\right]=? \\ $$$$\: \\ $$ Commented by gunawan last updated on…

Question-66476

Question Number 66476 by aliesam last updated on 15/Aug/19 Commented by kaivan.ahmadi last updated on 15/Aug/19 $${t}=\mathrm{4}{x}+\mathrm{1}\Rightarrow \\ $$$$\frac{\left({t}−\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow\frac{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} \left(\sqrt{{t}}+\mathrm{1}\right)^{\mathrm{2}} }{\left(\sqrt{{t}}−\mathrm{1}\right)^{\mathrm{2}} }={t}+\mathrm{2}\Rightarrow \\…