Question Number 150224 by mnjuly1970 last updated on 10/Aug/21 Answered by Olaf_Thorendsen last updated on 10/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\mathrm{1}+\lfloor\frac{{x}}{\mathrm{1}−{x}}\rfloor} \\ $$$$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{1}}{\mathrm{1}+\lfloor{u}\rfloor}.\frac{{du}}{\left(\mathrm{1}+{u}\right)^{\mathrm{2}} } \\…
Question Number 150180 by jlewis last updated on 10/Aug/21 $$\mathrm{show}\:\mathrm{that}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{Sin}\:\mathrm{x}/\mathrm{x}\:=\mathrm{1} \\ $$$$ \\ $$ Answered by liberty last updated on 10/Aug/21 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\right)=\frac{\mathrm{xcos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\: \\ $$…
Question Number 19085 by 433 last updated on 04/Aug/17 $$\mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right)=\sqrt{\mathrm{f}_{\mathrm{n}−\mathrm{1}} \left(\mathrm{x}\right)×\left(\mathrm{f}_{\mathrm{n}−\mathrm{1}} \left(\mathrm{x}\right)\right)'} \\ $$$$\mathrm{f}_{\mathrm{1}} \left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2017}} +\mathrm{x}^{\mathrm{8}} +\mathrm{x}^{\mathrm{4}} \\ $$$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}f}_{\mathrm{n}} \left(\mathrm{x}\right)=? \\ $$ Terms…
Question Number 150125 by mnjuly1970 last updated on 09/Aug/21 $$ \\ $$$$\:\:\:\:\int\:\frac{{x}^{\:\mathrm{2}} }{\:\sqrt{\mathrm{4}+{x}^{\:\mathrm{4}} }}\:{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84543 by niroj last updated on 14/Mar/20 $$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\:,\boldsymbol{\mathrm{c}}\:\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\overset{\mathrm{lim}} {\:}}\:\frac{\left(\boldsymbol{\mathrm{a}}\:+\boldsymbol{\mathrm{b}}\:\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{x}−\boldsymbol{\mathrm{c}}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} }=\mathrm{1} \\ $$ Commented by mr W last updated on 14/Mar/20…
Question Number 84442 by Power last updated on 13/Mar/20 Answered by john santu last updated on 13/Mar/20 $$\mathrm{let}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{3x}^{\mathrm{5x}} } \:\Rightarrow\mathrm{ln}\left(\mathrm{y}\right)=\:\mathrm{ln}\left(\mathrm{x}^{\mathrm{3x}^{\mathrm{5x}} } \right) \\ $$$$\mathrm{let}\:\mathrm{3x}^{\mathrm{5x}} \:=\:\mathrm{g}\left(\mathrm{x}\right)…
Question Number 18906 by Arnab Maiti last updated on 01/Aug/17 $$\mathrm{calculate}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\:\mathrm{where}\: \\ $$$$\mathrm{y}=\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{a}+\mathrm{b}\:\mathrm{cosx}}{\mathrm{b}+\mathrm{a}\:\mathrm{cosx}}\:\left(\mathrm{b}>\mathrm{a}\right) \\ $$ Answered by ajfour last updated on 01/Aug/17 $$\:\mathrm{y}=\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{a}+\mathrm{bcos}\:\mathrm{x}}{\mathrm{b}+\mathrm{acos}\:\mathrm{x}}\right)…
Question Number 18905 by Arnab Maiti last updated on 01/Aug/17 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{differentiation} \\ $$$$\mathrm{of}\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\:\mathrm{with}\:\mathrm{respect} \\ $$$$\mathrm{to}\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }\:\:\mathrm{is}\:\:\frac{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}{\mathrm{x}^{\mathrm{6}} } \\ $$ Terms…
Question Number 84327 by sahnaz last updated on 11/Mar/20 $$\int\frac{\mathrm{3}−\mathrm{7u}}{\mathrm{7u}^{\mathrm{2}} −\mathrm{7}}\mathrm{du} \\ $$ Answered by 20092104 last updated on 15/Mar/20 $$\int\frac{\mathrm{3}−\mathrm{7}{u}}{\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}}{du} \\ $$$$=\int\frac{\mathrm{3}−\mathrm{7}{u}}{\mathrm{7}\left({u}^{\mathrm{2}} −\mathrm{1}\right)}{du}…
Question Number 84326 by sahnaz last updated on 11/Mar/20 $$\int\frac{\mathrm{3}−\mathrm{7u}}{\mathrm{7u}^{\mathrm{2}} −\mathrm{7}}\mathrm{du} \\ $$ Answered by TANMAY PANACEA last updated on 11/Mar/20 $$\frac{\mathrm{3}}{\mathrm{7}}\int\frac{{du}}{\left({u}+\mathrm{1}\right)\left({u}−\mathrm{1}\right)}−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{d}\left(\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}\right)}{\mathrm{7}{u}^{\mathrm{2}} −\mathrm{7}} \\…