Question Number 18022 by ibraheem160 last updated on 13/Jul/17 $${The}\:{first}\:{term}\:{of}\:{an}\:{A}.{P}\:\:{is}\:{log}^{{a}} \:{and}\:{second}\:{term}\:{is}\: \\ $$$${log}^{{b}} .{show}\:{that}\:{the}\:{sum}\:{of}\:{first}\:{n}\:{terms}\:{in}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{log}\left[\frac{{b}^{{n}\left({n}−\mathrm{1}\right)} }{{a}^{{n}\left(−\mathrm{3}\right)} }\right] \\ $$ Answered by prakash jain last…
Question Number 83556 by M±th+et£s last updated on 03/Mar/20 $${find}\:{the}\:{value}\:{of}\:\:\left({b}\right)\:{wich}\:{makes}\:{the} \\ $$$${line}\:{y}={b}\:{divide}\:{the}\:{tow}\:{funtions}\:{into} \\ $$$${tow}\:{equal}\:{parts} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{f}\left({x}\right)=\mathrm{9}−{x}^{\mathrm{2}} \:,\:{g}\left({x}\right)=\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){f}\left({x}\right)=\mathrm{9}−\mid{x}\mid\:,\:{g}\left({x}\right)=\mathrm{0} \\ $$…
Question Number 83554 by Power last updated on 03/Mar/20 Answered by MJS last updated on 03/Mar/20 $${x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} −\mathrm{8}{x}+\frac{\mathrm{17}}{\mathrm{5}}=\mathrm{0} \\ $$$$\mathrm{let}\:{x}={t}−\mathrm{1} \\ $$$${t}^{\mathrm{4}} −\mathrm{6}{t}^{\mathrm{2}} +\frac{\mathrm{42}}{\mathrm{5}}=\mathrm{0}…
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Question Number 18015 by alex041103 last updated on 13/Jul/17 $${Just}\:{for}\:{fun} \\ $$$${Prove}\:{that}\:{there}\:{are}\:{no}\:{real}\:{numbers}\:{A}\:{and}\:{B}\:{that} \\ $$$${satisfy}\: \\ $$$${sinA}=\frac{\mathrm{2}}{{sinB}} \\ $$ Commented by alex041103 last updated on 13/Jul/17…
Question Number 149081 by Integrals last updated on 02/Aug/21 Answered by Ar Brandon last updated on 02/Aug/21 $$\phi=\int\frac{{d}\beta}{\mathrm{2}−\mathrm{3sin}\beta}\:,\:{t}=\mathrm{tan}\frac{\beta}{\mathrm{2}} \\ $$$$\:\:\:=\int\frac{\mathrm{2}}{\mathrm{2}−\mathrm{3}\left(\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right)}\centerdot\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }=\int\frac{{dt}}{{t}^{\mathrm{2}} −\mathrm{3}{t}+\mathrm{1}} \\ $$$$\:\:\:=\int\frac{{dt}}{\left({t}−\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 149080 by Integrals last updated on 02/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 149077 by mnjuly1970 last updated on 02/Aug/21 $$ \\ $$$$\:\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}\:\left(\:\mathrm{1}+\:\sqrt{{x}}\:\right)}{\mathrm{1}+{x}}\:{dx}\:=? \\ $$$$\:…..{m}.{n}….. \\ $$ Answered by mindispower last updated on 02/Aug/21…
Question Number 83542 by Power last updated on 03/Mar/20 Answered by john santu last updated on 03/Mar/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}^{\mathrm{2x}−\mathrm{1}} } \\ $$$$\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2001}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}^{\frac{\mathrm{2}}{\mathrm{2001}}−\mathrm{1}} } \\ $$$$\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{2001}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}^{\frac{\mathrm{2}}{\mathrm{2001}}−\mathrm{1}} }…
Question Number 83543 by Power last updated on 03/Mar/20 Commented by john santu last updated on 03/Mar/20 $$\mathrm{let}\:\mathrm{1}+\mathrm{2x}+\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}^{\mathrm{3}} +\mathrm{5x}^{\mathrm{4}} +…\:=\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\:\int\left(\mathrm{1}+\mathrm{2x}+\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}^{\mathrm{3}} +…\right)\mathrm{dx}…