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Author: Tinku Tara

lim-n-k-1-n-j-1-n-2-sin-k-n-sin-k-n-2-1-n-2-j-ln-1-1-n-

Question Number 212311 by MrGaster last updated on 09/Oct/24 $$ \\ $$$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\:\underset{{j}=\mathrm{1}} {\overset{{n}^{\mathrm{2}} } {\sum}}\:\mathrm{sin}\frac{{k}}{{n}}\centerdot\mathrm{sin}\frac{{k}}{{n}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} +{j}}}\mathrm{l}{n}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$ Terms of Service…

Question-212291

Question Number 212291 by hardmath last updated on 08/Oct/24 Commented by hardmath last updated on 08/Oct/24 $$\mathrm{m}\left(\angle\mathrm{BCD}\right)\:=\:\mathrm{90}° \\ $$$$\mid\mathrm{AB}\mid\:=\:\mid\mathrm{AC}\mid \\ $$$$\mathrm{AC}\:\cap\:\mathrm{BD}\:=\:\mathrm{K} \\ $$$$\mathrm{Area}\left(\mathrm{ABCD}\right)\:=\:? \\ $$…

Question-212239

Question Number 212239 by Spillover last updated on 07/Oct/24 Answered by Ghisom last updated on 08/Oct/24 $$\int\frac{\mathrm{e}^{−{x}/\mathrm{2}} \sqrt{\mathrm{1}−\mathrm{sin}\:{x}}}{\mathrm{1}+\mathrm{cos}\:{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\right] \\ $$$$=\int\frac{\mathrm{e}^{−\mathrm{arctan}\:{t}} \left({t}−\mathrm{1}\right)}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}{dt}= \\…

sin-1-12-13-cos-1-3-5-tan-1-63-16-

Question Number 212233 by Davidtim last updated on 07/Oct/24 $$\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{12}}{\mathrm{13}}\right)+\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{5}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{63}}{\mathrm{16}}\right)=? \\ $$ Commented by Davidtim last updated on 07/Oct/24 $${I}\:{kindly}\:{request}\:{you}\:{for}\:{helping} \\ $$…