Question Number 30514 by abdo imad last updated on 22/Feb/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\prod_{{k}=\mathrm{1}} ^{{n}} \:\left(\mathrm{1}−\:\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{3}} }\right).\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30511 by abdo imad last updated on 22/Feb/18 $${find}\:\:{lim}_{{x}\rightarrow+\infty} \:\:{e}^{{x}} \:\left[\frac{\mathrm{1}}{{x}}\right]. \\ $$ Commented by abdo imad last updated on 24/Feb/18 $${for}\:{x}>\mathrm{1}\:\Rightarrow\:\mathrm{0}<\frac{\mathrm{1}}{{x}}<\mathrm{1}\:\Rightarrow\:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\:\Rightarrow\:\forall{x}>\mathrm{1}\:{e}^{{x}} \:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\Rightarrow…
Question Number 161583 by cortano last updated on 19/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{sin}\:\frac{\pi}{{x}}}{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}}\:=? \\ $$$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} −\mathrm{8}+\mathrm{sin}\:\pi{x}}{\mathrm{2}−{x}}=? \\ $$$$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{cos}\:\left(\frac{\pi}{{x}+\mathrm{1}}\right)}=? \\ $$ Commented by blackmamba…
Question Number 30510 by abdo imad last updated on 22/Feb/18 $${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}^{+\:} } \:\:\:\:\sqrt{{x}}\:\left[\:\frac{\mathrm{1}}{{x}}\right]\:\:{and}\:{lim}_{{x}\rightarrow+\infty} \:\:\frac{\left[{x}\right]}{{x}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30504 by abdo imad last updated on 22/Feb/18 $${find}\:{lim}_{{x}\rightarrow\infty} \:{x}^{\mathrm{2}} \left(\:{e}^{\frac{\mathrm{1}}{{x}}} \:\:\:−\:{e}^{\frac{\mathrm{1}}{{x}+\mathrm{1}}} \right)\:. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $$…
Question Number 30502 by abdo imad last updated on 22/Feb/18 $${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \left({sinx}\:+{cosx}\right)^{\frac{\mathrm{1}}{{x}}} \:\:. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $$\left({sinx}+{cosx}\right)^{\mathrm{1}/{x}} ={e}^{\frac{{ln}\left({sinx}+{cosx}\right)}{{x}}} \\…
Question Number 30493 by abdo imad last updated on 22/Feb/18 $${study}\:{tbe}\:{sequence}\:\:{x}_{{n}+\mathrm{1}} \:=\:\frac{\mathrm{1}}{\mathrm{2}−{x}_{{n}} }\:{with}\:{x}_{{o}} \neq\mathrm{2}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30491 by abdo imad last updated on 22/Feb/18 $${let}\:{A}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{n}}{{n}^{\mathrm{2}} \:+{k}^{\mathrm{2}} }\:{find}\:\:{lim}_{{n}\rightarrow\infty} {A}_{{n}} . \\ $$ Terms of Service Privacy Policy…
Question Number 30487 by abdo imad last updated on 22/Feb/18 $${for}\:{n}\geqslant\mathrm{2}\:{let}\:\:{x}_{{n}} =\:\:\frac{\sum_{{k}=\mathrm{1}} ^{{n}} \:\left[{lnk}\right]}{{ln}\left({n}!\right)}\:\:{find}\:{lim}_{{n}\rightarrow\infty} {x}_{{n}} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161553 by qaz last updated on 19/Dec/21 $$\underset{\mathrm{t}\rightarrow+\infty} {\mathrm{lim}t}\underset{\mathrm{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\:\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} }}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com