Question Number 145888 by bramlexs22 last updated on 09/Jul/21 Answered by liberty last updated on 09/Jul/21 $${f}\left({x}\right)={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}\:;\:{a},{b},{c}\:\in{R} \\ $$$${f}\:'\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{ax}+{b} \\ $$$${f}\:''\left({x}\right)=\mathrm{6}{x}+\mathrm{2}{a}\: \\…
Question Number 80332 by ~blr237~ last updated on 02/Feb/20 $$\:\:{let}\:\alpha\:\in\mathbb{R}\:\:{and}\:\:\:\:{a}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{sin}\left({k}\alpha\right)}{{n}+{k}} \\ $$$${Find}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:{a}_{{n}} \: \\ $$ Commented by Rio Michael last updated…
Question Number 80334 by ~blr237~ last updated on 02/Feb/20 $$\:{let}\:\:\:{f}\in{L}^{\mathrm{1}} \left(\mathbb{R}\right)\:\:\: \\ $$$${let}\:\:{u}_{{n}} =\:\int_{{a}} ^{{b}} {f}\left({t}\right){sin}\left({nt}\right){dt}\:,\:{v}_{{n}} =\int_{{a}} ^{{b}} \frac{{f}\left({t}\right)}{{t}}{sin}\left({nt}\right)\: \\ $$$$\left.\mathrm{1}\right){Prove}\:{that}\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{u}_{{n}} =\mathrm{0} \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:{in}\:{term}\:{of}\:{a},{b},{f}\left(\mathrm{0}\right)\:{the}\:{value}\:{of}\:\:\underset{{n}\rightarrow\infty}…
Question Number 80312 by TawaTawa last updated on 02/Feb/20 Commented by mr W last updated on 02/Feb/20 $${what}\:{is}\:\left\{…\right\}\:{here}\:? \\ $$ Commented by TawaTawa last updated…
Question Number 80300 by john santu last updated on 02/Feb/20 Commented by ~blr237~ last updated on 02/Feb/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{x}}=\mathrm{0}^{−\:\:} \:\:{and}\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{x}}=−\infty\:\: \\ $$$$\left.\underset{{x}\rightarrow\mathrm{0}^{−} }…
Question Number 145828 by ArielVyny last updated on 08/Jul/21 $$\int\frac{\mathrm{1}}{{x}^{\alpha} +{a}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145827 by qaz last updated on 08/Jul/21 $$\mathrm{Use}\:\mathrm{Abel}\:\mathrm{summation}\:\mathrm{to}\:\mathrm{evaluate}\::: \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2n}−\mathrm{1}\right)\centerdot\mathrm{2}^{\mathrm{n}} }=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{ln}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right) \\ $$ Answered by Ar Brandon last updated on 08/Jul/21…
Question Number 145777 by Engr_Jidda last updated on 08/Jul/21 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $$\int\frac{\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }{dx}=\int\frac{\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{\left(\mathrm{1}−\mathrm{3}{x}\right)\left(\mathrm{1}+\mathrm{3}{x}\right)}{dx} \\…
Question Number 145779 by Engr_Jidda last updated on 08/Jul/21 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\int_{\mathrm{0}} ^{\mathrm{1}} \left({e}^{{t}} +{e}^{−{t}} −\mathrm{2}\right)\frac{{dt}}{\mathrm{1}−{cosx}} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $${e}^{{t}}…
Question Number 145776 by Engr_Jidda last updated on 08/Jul/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{{x}} {cosxdx} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{{x}}…