Question Number 2054 by Yozzi last updated on 01/Nov/15 $${Find}\:{all}\:{real}\:{solutions}\:{y}\:{to}\:{the}\:{equation} \\ $$$$\:\:\:\:{sin}\left(\frac{{dy}}{{dx}}\right)+{sin}\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)=\mathrm{0}\:. \\ $$$${For}\:{each}\:{solution}\:{determine}\:{the}\:{value}\:{of} \\ $$$${Q}={max}\left(\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{sin}\left(\frac{{d}^{{r}} {y}}{{dx}^{{r}} }\right)\right),\:{giving}\:{the}\:{value}\left({s}\right) \\ $$$${of}\:{x}\:{for}\:{which}\:{Q}\:{arises}. \\…
Question Number 133127 by abdomsup last updated on 19/Feb/21 $${find}\:{lim}_{{n}\rightarrow\infty} \int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {lnx}\:{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 19/Feb/21 $$\underset{{n}\rightarrow\infty}…
Question Number 2052 by Yozzi last updated on 01/Nov/15 $${Find}\:{the}\:{solution}\:{of}\:{the}\:{d}.{e} \\ $$$$\:\left({sinhx}\right)\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} +\mathrm{2}\frac{{dy}}{{dx}}−{sinhx}=\mathrm{0} \\ $$$${which}\:{satisfies}\:{y}=\mathrm{0}\:{at}\:{x}=\mathrm{0}. \\ $$ Commented by prakash jain last updated on 01/Nov/15…
Question Number 133121 by abdomsup last updated on 19/Feb/21 $${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{\:\sqrt{{k}}} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \left({n}+\rightarrow\infty\right) \\ $$ Answered by mindispower last updated on 19/Feb/21…
Question Number 2051 by Yozzi last updated on 01/Nov/15 $${Solve}\:{the}\:{d}.{e}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \frac{{dy}}{{dx}}+{xy}+{x}^{\mathrm{2}} {y}^{\mathrm{2}} =\mathrm{1} \\ $$$${by}\:{letting}\:{y}=\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{v}}\:{where} \\ $$$${v}\:{is}\:{a}\:{function}\:{of}\:{x}.\: \\ $$ Answered by 123456 last…
Question Number 133120 by abdomsup last updated on 19/Feb/21 $${calculate}\:{A}_{{n}} =\:\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.} \:\:\frac{{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } }{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{3}}}{dxdy} \\ $$$${and}\:{lim}_{{n}\rightarrow\infty} {A}_{{n}} \\ $$ Terms of Service…
Question Number 2050 by Yozzi last updated on 01/Nov/15 $${Solve}\:{the}\:{d}.{e} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{{dx}}−{y}−\mathrm{3}{y}^{\mathrm{2}} =−\mathrm{2}\: \\ $$$${by}\:{letting}\:{y}=\frac{−\mathrm{1}}{\mathrm{3}{u}}\left(\frac{{du}}{{dx}}\right). \\ $$ Answered by 123456 last updated on 01/Nov/15 $${y}'=\frac{{dy}}{{dx}}…
Question Number 133123 by abdomsup last updated on 19/Feb/21 $${find}\:\int\:\:\frac{{x}^{\mathrm{2}} {dx}}{{x}^{\mathrm{3}} −\mathrm{2}{x}+\mathrm{1}} \\ $$ Answered by Ñï= last updated on 19/Feb/21 $$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{3}} −\mathrm{2}{x}+\mathrm{1}}{dx} \\…
Question Number 133122 by abdomsup last updated on 19/Feb/21 $${let}\:{V}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} +\mathrm{1}}} \\ $$$${find}\:{a}\:{ewivalent}\:{of}\:{V}_{{n}} \left({n}\smile\infty\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 133117 by SOMEDAVONG last updated on 19/Feb/21 $$\int\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{3}} \mathrm{x}}\mathrm{dx}=? \\ $$ Answered by bemath last updated on 19/Feb/21 $$=\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cot}\:\mathrm{x}\:\mathrm{csc}\:\mathrm{x}\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{sec}\:\mathrm{x}−\mathrm{cot}\:\mathrm{x}\mid\:+\:\mathrm{C} \\ $$ Terms of…