Question Number 125638 by aurpeyz last updated on 12/Dec/20 Answered by mathmax by abdo last updated on 12/Dec/20 $$\mathrm{S}\:=\frac{\mathrm{3}}{\mathrm{3}}−\frac{\mathrm{5}}{\mathrm{5}^{\mathrm{2}} }+\frac{\mathrm{7}}{\mathrm{5}^{\mathrm{3}} }−\frac{\mathrm{9}}{\mathrm{5}^{\mathrm{4}} }+…\Rightarrow\mathrm{S}\:=\mathrm{1}+\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \frac{\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{a}_{\mathrm{n}}…
Question Number 125641 by aurpeyz last updated on 12/Dec/20 Answered by Dwaipayan Shikari last updated on 12/Dec/20 $${S}=\mathrm{2}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{8}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{11}}{\mathrm{2}^{\mathrm{3}} }+… \\ $$$$\frac{{S}}{\mathrm{2}}=\:\:\:\:\:\:\frac{\mathrm{2}}{\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{8}}{\mathrm{2}^{\mathrm{3}} }+.. \\…
Question Number 125639 by aurpeyz last updated on 12/Dec/20 Commented by ZiYangLee last updated on 13/Dec/20 $$\mathrm{A}\:\mathrm{more}\:\mathrm{alternative}\:\mathrm{ways}: \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{x}^{{n}} =\frac{\mathrm{1}}{\mathrm{1}−{x}}−\mathrm{1} \\ $$$$\Rightarrow{f}'\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 125637 by aurpeyz last updated on 12/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125636 by Eric002 last updated on 12/Dec/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\int_{\mathrm{0}} ^{{sin}\:{x}} {sin}\frac{\mathrm{1}}{{t}}\:{cos}\:{t}^{\mathrm{2}} \:{dt} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60095 by Kunal12588 last updated on 17/May/19 Commented by Kunal12588 last updated on 17/May/19 $${find}\:{Domain} \\ $$ Answered by tanmay last updated on…
Question Number 125621 by ZiYangLee last updated on 12/Dec/20 $$\mathrm{Consider}\:\mathrm{a}\:\mathrm{continuously}\:\mathrm{differentiable} \\ $$$$\mathrm{function}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\mathrm{and}\:{f}\left(\mathrm{1}\right)=\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({f}'\left({x}\right)\right)^{\mathrm{2}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Terms of Service…
Question Number 191151 by TUN last updated on 19/Apr/23 $${f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right)={x}^{\mathrm{2}} \\ $$$$=>{f}\left({x}\right)=¿ \\ $$ Answered by Rasheed.Sindhi last updated on 19/Apr/23 $${f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right)={x}^{\mathrm{2}} …….\left({i}\right) \\ $$$${Replacing}\:{x}\:{by}\:\mathrm{1}−{x}:…
Question Number 191131 by TUN last updated on 18/Apr/23 Answered by a.lgnaoui last updated on 19/Apr/23 $$\bigtriangleup=\left(\mathrm{2m}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{m}^{\mathrm{2}} −\mathrm{6}\right)=\mathrm{25}−\mathrm{4m} \\ $$$$\bigtriangleup>\mathrm{0}\:\:\:\Rightarrow\mathrm{pour}\:\:\:\:\mathrm{m}<\frac{\mathrm{25}}{\mathrm{4}}\:\:\:\:\:\:\mathrm{2}\:\mathrm{solutions} \\ $$$$\mathrm{x}_{\mathrm{1}} =\frac{\mathrm{2m}−\mathrm{1}−\sqrt{\mathrm{25}−\mathrm{4m}}}{\mathrm{2}};\:\:\mathrm{x}_{\mathrm{2}} =\frac{\mathrm{2m}−\mathrm{1}+\sqrt{\mathrm{25}−\mathrm{4m}}}{\mathrm{2}}…
Question Number 191121 by SANOGO last updated on 18/Apr/23 Terms of Service Privacy Policy Contact: info@tinkutara.com