Question Number 21612 by x² – y²@gmail.com last updated on 29/Sep/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21581 by mondodotto@gmail.com last updated on 28/Sep/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21566 by mondodotto@gmail.com last updated on 27/Sep/17 Commented by mrW1 last updated on 27/Sep/17 $$\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{4}}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{a}=\mathrm{2} \\ $$ Commented by…
Question Number 152617 by eman_64 last updated on 30/Aug/21 Commented by mr W last updated on 30/Aug/21 $${L}=\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\frac{−\mathrm{cos}\:\left(\frac{\pi}{\mathrm{6}}−{x}\right)}{−\mathrm{4cos}\:{x}}=\frac{\mathrm{1}}{\mathrm{4}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}} \\ $$ Terms of Service Privacy…
Question Number 152608 by ZiYangLee last updated on 30/Aug/21 $$\mathrm{By}\:\mathrm{using}\:\mathrm{the}\:\mathrm{substitution}\:{x}=\mathrm{cos}\:\mathrm{2}\theta, \\ $$$$\mathrm{prove}\:\mathrm{that}\:\int\:\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx}\:=\:−\mathrm{sin}\:\mathrm{2}\theta−\mathrm{2}\theta+{C} \\ $$ Answered by Olaf_Thorendsen last updated on 30/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\sqrt{\:\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx} \\ $$$$\mathrm{F}\left(\theta\right)\:=\:\int\sqrt{\:\frac{\mathrm{1}+\mathrm{cos2}\theta}{\mathrm{1}−\mathrm{cos2}\theta}}\:\left(−\mathrm{2sin2}\theta{d}\theta\right) \\…
Question Number 21510 by x² – y²@gmail.com last updated on 25/Sep/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21503 by mondodotto@gmail.com last updated on 25/Sep/17 Answered by $@ty@m last updated on 26/Sep/17 $${Let}\:\mathrm{4}{x}^{\mathrm{2}} ={t} \\ $$$$\Rightarrow\mathrm{8}{xdx}={dt} \\ $$$${Change}\:{of}\:{limits}: \\ $$$${As}\:{x}\rightarrow\mathrm{4},\:{t}\rightarrow\mathrm{64} \\…
Question Number 21504 by mondodotto@gmail.com last updated on 25/Sep/17 Answered by $@ty@m last updated on 26/Sep/17 $${ATQ} \\ $$$$\boldsymbol{{S}}_{{n}} =\left(−\mathrm{1}\right)+\mathrm{1}+\mathrm{3}+\mathrm{5}+……+\left(\mathrm{2}{n}−\mathrm{3}\right) \\ $$$$\left({i}\right)\:\boldsymbol{{S}}_{\mathrm{50}} =\frac{\mathrm{50}}{\mathrm{2}}\left\{\left(−\mathrm{1}\right)+\left(\mathrm{2}×\mathrm{50}−\mathrm{3}\right)\right\} \\ $$$$=\mathrm{25}\left(−\mathrm{1}+\mathrm{97}\right)…
Question Number 152571 by Gbenga last updated on 29/Aug/21 $$\:\mathrm{2}\boldsymbol{{log}}\mathrm{4}^{\boldsymbol{{x}}} +\mathrm{9}\boldsymbol{{logx}}^{\mathrm{4}} =\mathrm{9} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$ Answered by mr W last updated on 29/Aug/21 $$\mathrm{log}\:\left(\mathrm{4}^{\mathrm{2}{x}}…
Question Number 152555 by Gbenga last updated on 29/Aug/21 $$\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}{k}}^{\mathrm{5}} =? \\ $$ Answered by EDWIN88 last updated on 29/Aug/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left({k}+\mathrm{1}\right)^{\mathrm{5}}…