Question Number 159598 by Ar Brandon last updated on 19/Nov/21 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sums}; \\ $$$${u}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{n}}{{nk}^{\mathrm{2}} +{k}+\mathrm{1}} \\ $$$${v}_{{n}} =\underset{\mathrm{1}\leqslant{k}\leqslant\mathrm{2}{n}} {\sum}\frac{{n}^{\mathrm{2}} }{{kn}^{\mathrm{2}} +{k}^{\mathrm{2}} } \\…
Question Number 28490 by A1B1C1D1 last updated on 26/Jan/18 $$\underset{\mathrm{x}\:\rightarrow\:\mathrm{a}} {\mathrm{lim}}\:\left(\frac{\mathrm{cos}\left(\mathrm{x}\right)\:−\:\mathrm{cos}\left(\mathrm{a}\right)}{\mathrm{x}\:−\:\mathrm{a}}\right) \\ $$$$ \\ $$$$\mathrm{Don}'\mathrm{t}\:\mathrm{use}\:\mathrm{L}'\mathrm{h}\bar {\mathrm{o}spital}\:\mathrm{rule}. \\ $$ Answered by $@ty@m last updated on 27/Jan/18…
Question Number 159549 by mathlove last updated on 18/Nov/21 Answered by Ar Brandon last updated on 18/Nov/21 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{3}^{{x}} \right)}{\mathrm{ln}\left(\mathrm{1}+\mathrm{2}^{{x}} \right)}=\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\mathrm{3}^{{x}} }{\mathrm{2}^{{x}} }=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{{x}}…
Question Number 28467 by Asad8992002 last updated on 26/Jan/18 Commented by abdo imad last updated on 26/Jan/18 $${for}\:{all}\:{x}\:{from}\:{R}\:{and}\:{x}>\mathrm{0}\:\:\:\:\:\:\:\:−\frac{\mathrm{1}}{{x}}\leqslant\:\frac{{sinx}}{{x}}\leqslant\:\frac{\mathrm{1}}{{x}}\:{but} \\ $$$${lim}_{{x}\rightarrow+\infty} \:\:−\frac{\mathrm{1}}{{x}}=\mathrm{0}\:\:{and}\:\:{lim}_{{x}\rightarrow+\infty} \:\frac{\mathrm{1}}{{x}}=\mathrm{0}\:\:{so} \\ $$$${lim}_{{x}\rightarrow+\infty} \:\frac{{sinx}}{{x}}\:={o}\:\:\:\:{and}\:{by}\:{the}\:{same}\:{method}\:{we}\:{prove}…
Question Number 159525 by mnjuly1970 last updated on 18/Nov/21 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\:{sin}^{\:\mathrm{3}} \left({x}\right)}{{x}^{\:\mathrm{3}} }\right)\:{ln}\left({x}\right){dx}=? \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 159522 by mathlove last updated on 18/Nov/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sin}\left({sinx}\right)}{{x}}=? \\ $$ Commented by cortano last updated on 18/Nov/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)}{\mathrm{sin}\:{x}}\:×\:\frac{\mathrm{sin}\:{x}}{{x}}\:=\:\mathrm{1} \\ $$ Terms…
Question Number 28437 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\:{sin}\:\left(\frac{\pi}{{x}}\right)\:\:\:{find}\:{f}^{\left({n}\right)} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28430 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}+\frac{{x}}{{n}}\right)^{{n}} {e}^{−\mathrm{2}{x}} {dx}\:\:\:{lim}_{{n}\rightarrow\propto} \:{A}_{{n}} ? \\ $$$$ \\ $$ Commented by abdo…
Question Number 28429 by abdo imad last updated on 25/Jan/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\int_{{x}+\mathrm{1}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:\frac{{t}^{\mathrm{2}} }{{ln}\left(\mathrm{1}+{t}\right)}{dt}\:\:. \\ $$ Commented by abdo imad last updated on 27/Jan/18…
Question Number 28426 by abdo imad last updated on 25/Jan/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\left(\mathrm{1}+{sinx}\right)^{\frac{\mathrm{1}}{{x}}} \:\:−{e}^{\mathrm{1}−\frac{{x}}{\mathrm{2}}} }{\left(\mathrm{1}+{tanx}\right)^{\frac{\mathrm{1}}{{x}}} −\:\:{e}^{\mathrm{1}−\frac{{x}}{\mathrm{2}}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com