Question Number 84954 by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}}\:−\:\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\frac{\mathrm{5}}{\mathrm{2}}} }\:=\:? \\ $$ Answered by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}}…
Question Number 150325 by mnjuly1970 last updated on 11/Aug/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{Solve}….. \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\boldsymbol{\phi}=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {cos}^{\:\mathrm{2}} \left({x}\:\right).\:{ln}\:\left({cot}\left(\:{x}\:\right)\right){dx}=?\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:…..{m}.{n}….. \\ $$ Answered by…
Question Number 150226 by mnjuly1970 last updated on 10/Aug/21 $$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\zeta\:\left(\mathrm{0}\:\right)\overset{?} {=}\:\frac{−\mathrm{1}}{\mathrm{2}}\:……….\blacksquare \\ $$$$\:\:\:\:\:\:\:{m}.{n}… \\ $$ Answered by Kamel last…
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)…