Question Number 126907 by Dwaipayan Shikari last updated on 25/Dec/20 $$\boldsymbol{{Merry}}\:\boldsymbol{{christmas}}\:!! \\ $$$$ \\ $$🎅🤶☃️🌄🎄🦌 $$ \\ $$$$ \\ $$🔔🔔🔔🔔🔔🔔🔔🔔🔔 🎄🎄🎄🎄🎄🎄🎄🎄 $$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\boldsymbol{{tanh}}^{−\mathrm{1}} \boldsymbol{{x}}}{\:\sqrt[{\mathrm{5}}]{\boldsymbol{{x}}}}\boldsymbol{{dx}}…
Question Number 192443 by Mastermind last updated on 18/May/23 $$\mathrm{Find}\:\mathrm{the}\:\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{16th}\:\mathrm{term} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{3}\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{4}\frac{\mathrm{3}}{\mathrm{4}}\:+\:\mathrm{6}\:+\:\mathrm{7}\frac{\mathrm{1}}{\mathrm{4}}\:… \\ $$ Answered by AST last updated on 18/May/23 $${S}_{\mathrm{16}} =\mathrm{8}\left(\mathrm{7}+\frac{\mathrm{75}}{\mathrm{4}}\right)=\mathrm{56}+\mathrm{150}=\mathrm{206} \\ $$…
Question Number 126904 by Mustafa2020 last updated on 25/Dec/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by mindispower last updated on 25/Dec/20 $$\geqslant\Sigma\int_{\mathrm{2}{k}\pi} ^{\mathrm{2}{k}\pi+\frac{\pi}{\mathrm{6}}}…
Question Number 192437 by MATHEMATICSAM last updated on 18/May/23 $$\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{1}}{{a}\:+\:{b}\:+\:{c}}\:.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{5}} }\:+\:\frac{\mathrm{1}}{{b}^{\mathrm{5}} }\:+\:\frac{\mathrm{1}}{{c}^{\mathrm{5}} }\:=\:\frac{\mathrm{1}}{{a}^{\mathrm{5}} \:+\:{b}^{\mathrm{5}} \:+\:{c}^{\mathrm{5}} }\:=\:\frac{\mathrm{1}}{\left({a}\:+\:{b}\:+\:{c}\right)^{\mathrm{5}} } \\ $$ Answered by Frix last…
Question Number 192433 by cortano12 last updated on 18/May/23 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{ln}\:\left(\mathrm{3x}+\mathrm{1}\right)\right)}{\mathrm{3x}^{\mathrm{6}} −\mathrm{tan}\:\left(\mathrm{3x}^{\mathrm{2}} \right)}=? \\ $$ Answered by mehdee42 last updated on 18/May/23 $${tip}\::{if}\:\:{u}\rightarrow\mathrm{0} \\ $$$$\Rightarrow\mathrm{1}−{cosu}\sim\frac{\mathrm{1}}{\mathrm{2}}{u}^{\mathrm{2}}…
Question Number 61363 by bhanukumarb2@gmail.com last updated on 01/Jun/19 Answered by tanmay last updated on 02/Jun/19 $${N}_{{r}} =\mathrm{2}^{\mathrm{2}{b}_{{n}} } −\mathrm{2}^{\mathrm{1}+{b}_{{n}} } .\mathrm{3}^{{b}_{{n}} } +\mathrm{3}^{\mathrm{2}{b}_{{n}} }…
Question Number 126896 by BHOOPENDRA last updated on 25/Dec/20 $${yy}''−\left({y}'\right)^{\mathrm{2}} ={e}^{{ax}\:} {find}\:{genral}\:{solution}? \\ $$ Commented by liberty last updated on 25/Dec/20 $${ok}\:{i}\:{try}\:{solve}\:{it}. \\ $$$$ \\…
Question Number 192429 by Spillover last updated on 17/May/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 192428 by Spillover last updated on 17/May/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126895 by mohammad17 last updated on 25/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com