Question Number 53311 by gunawan last updated on 20/Jan/19 $$\mathrm{If}\:\int\:\frac{\mathrm{4}{e}^{{x}} +\mathrm{6}{e}^{−{x}} }{\mathrm{9}{e}^{{x}} −\mathrm{4}{e}^{−{x}} }\:{dx}={Ax}+{B}\:\mathrm{log}\left(\mathrm{9}{e}^{\mathrm{2}{x}} −\mathrm{4}\right)+{C} \\ $$$$\mathrm{then} \\ $$$${A}=… \\ $$$${B}=… \\ $$$${C}=… \\ $$…
Question Number 184320 by Rasheed.Sindhi last updated on 05/Jan/23 $$\boldsymbol{\mathrm{All}}-\boldsymbol{\mathrm{time}}\:\boldsymbol{\mathrm{Universal}}\:\boldsymbol{\mathrm{Formula}} \\ $$$$\:\begin{array}{|c|}{\boldsymbol{\mathrm{OLD}}+\mathrm{1}=\boldsymbol{\mathrm{NEW}}}\\\hline\end{array}\: \\ $$$$\boldsymbol{{Year}}:-\boldsymbol{\mathcal{T}{he}}\:\boldsymbol{{above}}\:\boldsymbol{{formula}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{applies}}\:\boldsymbol{{every}}\:\boldsymbol{{year}}. \\ $$$$\boldsymbol{{Month}}:-\boldsymbol{{It}}\:\boldsymbol{{also}}\:\boldsymbol{{applies}}\:\boldsymbol{{every}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{month}}. \\ $$$$\boldsymbol{{Day}}:-\boldsymbol{{It}}\:\boldsymbol{{also}}\:\boldsymbol{{applies}}\:\boldsymbol{{every}}\:\boldsymbol{{day}}. \\ $$$$…. \\…
Question Number 184311 by Noorzai last updated on 05/Jan/23 Answered by SEKRET last updated on 05/Jan/23 $$\:\:\:\frac{\boldsymbol{\pi}}{\:\mathrm{24}}\boldsymbol{\mathrm{ln}}\left(\mathrm{1351}+\mathrm{780}\sqrt{\mathrm{3}}\right)\:\:−\:\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{12}\sqrt{\mathrm{3}}} \\ $$ Terms of Service Privacy Policy…
Question Number 184307 by Mastermind last updated on 05/Jan/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{boundary}−\mathrm{value} \\ $$$$\mathrm{problem}\:\mathrm{y}''+\lambda\mathrm{y}=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}, \\ $$$$\mathrm{y}\left(\mathrm{L}\right)=\mathrm{0}\:\mathrm{has}\:\mathrm{only}\:\mathrm{the}\:\mathrm{trival}\:\mathrm{solution} \\ $$$$\mathrm{y}=\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{cases}\:\lambda=\mathrm{0}\:\mathrm{and}\:\lambda<\mathrm{0}. \\ $$$$\mathrm{let}\:\mathrm{L}\:\mathrm{be}\:\mathrm{a}\:\mathrm{non}−\mathrm{zero}\:\mathrm{real}\:\mathrm{number}. \\ $$$$ \\ $$$$ \\ $$$$? \\…
Question Number 184306 by Mastermind last updated on 05/Jan/23 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{value}\: \\ $$$$\mathrm{problem}\:\mathrm{y}^{''} −\mathrm{2y}'+\mathrm{2y}=\mathrm{0},\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{a}\right)=\mathrm{c} \\ $$$$,\mathrm{y}\left(\mathrm{b}\right)=\mathrm{d}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{If}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{a}\:\mathrm{unique} \\ $$$$\mathrm{solution},\:\mathrm{how}\:\mathrm{are}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{related}? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{If}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}, \\ $$$$\mathrm{how}\:\mathrm{are}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\:\mathrm{related}? \\ $$$$…
Question Number 184264 by Noorzai last updated on 04/Jan/23 Answered by ARUNG_Brandon_MBU last updated on 04/Jan/23 $${I}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{tx}} \frac{\mathrm{sin}{mx}}{{x}}{dx}\:\Rightarrow{I}'\left({t}\right)=−\int_{\mathrm{0}} ^{\infty} {e}^{−{tx}} \mathrm{sin}{mxdx} \\ $$$$\Rightarrow{I}'\left({t}\right)=−\left[\frac{{e}^{−{tx}}…
Question Number 118685 by warllaybabs last updated on 19/Oct/20 $$\boldsymbol{{Converting}}\:\boldsymbol{{decimal}}\:\boldsymbol{{numbers}}\:\boldsymbol{{to}}\:\boldsymbol{{base}}\:\mathrm{10} \\ $$ Commented by MJS_new last updated on 19/Oct/20 $$“\mathrm{decimal}\:\mathrm{number}''\:\mathrm{means},\:\mathrm{number}\:\mathrm{has}\:\mathrm{base}\:\mathrm{10} \\ $$ Terms of Service…
Question Number 184218 by katana last updated on 04/Jan/23 Answered by Rasheed.Sindhi last updated on 04/Jan/23 $$\mathrm{Suppose}\:\mathrm{car}\:\mathrm{catches}\:\mathrm{the}\:\mathrm{bus}\:\mathrm{after}\:\mathrm{x} \\ $$$$\mathrm{hours}. \\ $$$$\bullet\mathrm{When}\:\mathrm{the}\:\mathrm{car}\:\mathrm{catces}\:\mathrm{the}\:\mathrm{bus},\mathrm{the}\:\mathrm{bus} \\ $$$$\mathrm{has}\:\mathrm{travelled}\:\mathrm{for}\:\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{x}\:\:\mathrm{hours},\left(\mathrm{while}\right. \\ $$$$\left.\mathrm{the}\:\mathrm{car}\:\mathrm{has}\:\mathrm{travelled}\:\mathrm{for}\:\mathrm{x}\:\mathrm{hours}.\right)…
Question Number 184188 by Mastermind last updated on 03/Jan/23 $$\mathrm{Differentiate},\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{x}−\mathrm{1}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{hi} \\ $$ Answered by SEKRET last updated on 03/Jan/23…
Question Number 184185 by Mastermind last updated on 03/Jan/23 $$\mathrm{Differentiate},\:\mathrm{y}=\left(\mathrm{log}_{\mathrm{e}} \mathrm{x}\right)^{\mathrm{x}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$ Answered by SEKRET last updated on…