Question Number 64347 by Rio Michael last updated on 16/Jul/19 $${Two}\:{consecutive}\:{integers}\:{between}\:{which}\:{a}\:{root}\:{of}\:{the}\:{equation} \\ $$$$\left.\:\mathrm{1}\right){x}^{\mathrm{3}} +{x}−\mathrm{16}=\mathrm{0}\: \\ $$$$\left.\mathrm{2}\right)\:{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}=\mathrm{0} \\ $$$${lies}\:{are}; \\ $$ Terms of Service Privacy…
Question Number 129883 by Algoritm last updated on 20/Jan/21 Answered by Olaf last updated on 20/Jan/21 $$\:{y}''+\mathrm{2}{y}'+{y}\:=\:\mathrm{2}{x}+\mathrm{1}−\mathrm{2}{e}^{−{x}} \:\left(\mathrm{1}\right) \\ $$$$\mathrm{Let}\:{y}\:=\:{u}\left({x}\right){e}^{−{x}} +{v}\left({x}\right) \\ $$$${y}'\:=\:\left({u}'−{u}\right){e}^{−{x}} +{v}' \\…
Question Number 129876 by LUFFY last updated on 20/Jan/21 Commented by Dwaipayan Shikari last updated on 20/Jan/21 $$\mathrm{2} \\ $$ Commented by LUFFY last updated…
Question Number 129874 by mohammad17 last updated on 20/Jan/21 Commented by mohammad17 last updated on 20/Jan/21 $${pleas}\:{sir}\:{help}\:{me} \\ $$ Answered by liberty last updated on…
Question Number 129872 by Bird last updated on 20/Jan/21 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{n}−{k}}{{n}^{\mathrm{2}} \:+{nk}+\mathrm{2009}} \\ $$$${determine}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 129873 by Bird last updated on 20/Jan/21 $${let}\:{m}={inff}\left({x}\right)_{{x}\in\left[{a},{b}\right]} \\ $$$${and}\:{M}={supf}\left({x}\right)_{{x}\in\left[{a},{b}\right]} \\ $$$${prove}\:{that}\:\left({b}−{a}\right)^{\mathrm{2}} \leqslant\int_{{a}} ^{{b}} {f}\left({x}\right){dx}.\int_{{a}} ^{{b}} \:\frac{{dx}}{{f}\left({x}\right)} \\ $$$$\leqslant\left({b}−{a}\right)^{\mathrm{2}} ×\frac{\left({m}+{M}\right)^{\mathrm{2}} }{\mathrm{4}{mM}} \\ $$…
Question Number 129870 by Bird last updated on 20/Jan/21 $${f}\:{continue}\:{on}\:\left[\bar {\mathrm{0}1}\right]\:{calculate} \\ $$$${lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}} \left({n}−{k}\right)\int_{\frac{{k}}{{n}}} ^{\frac{{k}+\mathrm{1}}{{n}}} {f}\left({x}\right){dx} \\ $$ Terms of Service Privacy Policy…
Question Number 129868 by Bird last updated on 20/Jan/21 $${find}\:{lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\frac{{k}}{\:\sqrt{\mathrm{4}{n}^{\mathrm{2}} −{k}^{\mathrm{2}} }} \\ $$ Answered by Ar Brandon last updated on 20/Jan/21…
Question Number 129869 by Bird last updated on 20/Jan/21 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{\left.\:\sqrt{\left({k}+{n}\right)\left({k}+\mathrm{1}+{n}\right.}\right)} \\ $$ Answered by mindispower last updated on 20/Jan/21 $$ \\ $$$$\frac{\mathrm{1}}{\left({k}+\mathrm{1}+{n}\right)}\leqslant\frac{\mathrm{1}}{\:\sqrt{{k}+{n}}.\sqrt{{k}+\mathrm{1}+{n}}}\leqslant\frac{\mathrm{1}}{{k}+{n}}…\mathrm{1}…
Question Number 129867 by Bird last updated on 20/Jan/21 $${calculate}\:\int\:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Answered by Olaf last updated on 20/Jan/21 $$\Omega\:=\:\int\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\:=\:\int\frac{{du}}{{u}^{\mathrm{3}} }…