Question Number 97781 by Ar Brandon last updated on 09/Jun/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{sequences}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{and}\:\left(\mathrm{v}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \mathrm{defined} \\ $$$$\mathrm{by}\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}!}\:\mathrm{and}\:\mathrm{v}_{\mathrm{n}} =\mathrm{u}_{\mathrm{n}} +\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}!\right)} \\ $$$$\mathrm{a}\backslash\:\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}}…
Question Number 163214 by cortano1 last updated on 05/Jan/22 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:{x}−\mathrm{2tan}\:{x}+{x}^{\mathrm{3}} }{\mathrm{6}{x}−\mathrm{2sin}\:\mathrm{3}{x}−\mathrm{9}{x}^{\mathrm{3}} }\:=? \\ $$ Commented by blackmamba last updated on 05/Jan/22 $$\:\mathcal{L}\:=\:\frac{\mathrm{5}}{\mathrm{81}} \\ $$…
Question Number 32137 by Joel578 last updated on 20/Mar/18 $$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\:\frac{{f}\left({x}\right){g}\left({x}\right)\:−\:\mathrm{3}{g}\left({x}\right)\:−\:\mathrm{3}}{{f}\left({x}\right)\:−\:\mathrm{3}\left({x}\:−\:\mathrm{5}\right)}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{g}'\left(\mathrm{5}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97577 by Rio Michael last updated on 08/Jun/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{4}{x}\:\mathrm{ln}{x}}{{x}−\mathrm{1}}\:=?? \\ $$ Commented by Dwaipayan Shikari last updated on 23/Jun/20 $$\mathrm{4}\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{xlog}\left(\mathrm{1}+{x}−\mathrm{1}\right)}{{x}−\mathrm{1}}=\mathrm{4} \\…
Question Number 32008 by gunawan last updated on 18/Mar/18 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\left(\frac{\mathrm{1}}{{n}}\right)^{{n}} +\left(\frac{\mathrm{2}}{{n}}\right)^{{n}} +..+\left(\frac{{n}}{{n}}\right)^{{n}} \right]=… \\ $$ Commented by JDamian last updated on 18/Mar/18 $${I}\:{guess}\:{the}\:{use}\:{of}\:\boldsymbol{{x}}\:{is}\:{a}\:{typo}. \\…
Question Number 163041 by qaz last updated on 03/Jan/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{n}}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }{\:\sqrt{\mathrm{n}}\mathrm{x}^{\mathrm{2}} }\mathrm{dx}−\sqrt{\pi}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163040 by qaz last updated on 03/Jan/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{n}!}{\mathrm{n}^{\mathrm{n}} }\left(\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}^{\mathrm{k}} }{\mathrm{k}!}−\underset{\mathrm{k}=\mathrm{n}+\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{n}^{\mathrm{k}} }{\mathrm{k}!}\right)=? \\ $$ Terms of Service Privacy Policy…
Question Number 163042 by qaz last updated on 03/Jan/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{n}}\int_{−\infty} ^{+\infty} \frac{\mathrm{cos}\:\mathrm{x}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }\mathrm{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163043 by qaz last updated on 03/Jan/22 $$\underset{\mathrm{x}\rightarrow−\infty} {\mathrm{lim}}\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{n}^{\mathrm{n}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163039 by qaz last updated on 03/Jan/22 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{n}}\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}\centerdot\mathrm{sin}^{\mathrm{2n}} \left(\mathrm{2}\pi\mathrm{x}\right)\mathrm{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com