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}} }}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30481 by abdo imad last updated on 22/Feb/18 $${find}\:{the}\:{value}\:{of}\:\:{s}_{\mathrm{1}} =\:\sum_{{p}\geqslant\mathrm{1},{q}\geqslant\mathrm{1}} \:\:\frac{\mathrm{1}}{{p}^{\mathrm{2}} {q}^{\mathrm{2}} }\:\:\:{and} \\ $$$${s}_{\mathrm{2}} =\:\:\sum_{{p}\geqslant\mathrm{1},{q}\geqslant\mathrm{1}\:,{pdivide}\:{q}} \:\:\frac{\mathrm{1}}{{p}^{\mathrm{2}} {q}^{\mathrm{2}} }\:. \\ $$ Terms of…
Question Number 30482 by abdo imad last updated on 22/Feb/18 $${find}\:\:{S}=\:\sum_{{p}\geqslant\mathrm{1},{q}\geqslant\mathrm{1}\:{and}\:\hat {{D}}\left({p},{q}\right)=\mathrm{1}} \:\:\frac{\mathrm{1}}{{p}^{\mathrm{2}} {q}^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161538 by mnjuly1970 last updated on 19/Dec/21 $$ \\ $$$${lim}_{\:{x}\:\rightarrow\:−\mathrm{2}\:\:} \left(\frac{\mathrm{2}+\:\mathrm{3}{x}\:+\:\mathrm{3}{x}^{\:\mathrm{2}} \:+\:{x}^{\:\mathrm{3}} }{\:{sin}\:\left(\:\frac{\pi{x}}{\mathrm{2}}\:\right)}\:\right)=? \\ $$$$\:\:\:\:−−−− \\ $$ Answered by Ar Brandon last updated…
Question Number 161533 by mathlove last updated on 19/Dec/21 Commented by cortano last updated on 19/Dec/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{x}}\right)^{\mathrm{2020}} −\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} −{x}}\right)^{\mathrm{2020}} }{{x}} \\ $$$$\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{1010}\left({x}^{\mathrm{2}}…
Question Number 161529 by qaz last updated on 19/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}\left(\left(\int_{\mathrm{1}} ^{+\infty} \frac{\mathrm{x}^{\mathrm{n}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{n}} +\mathrm{1}\right)}\mathrm{dx}\right)^{\mathrm{n}} −\frac{\mathrm{1}}{\mathrm{2}}\right)=? \\ $$ Terms of Service Privacy Policy…