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)=? \\ $$ Terms of Service Privacy Policy…
Question Number 95980 by john santu last updated on 29/May/20 $$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\sqrt{\mathrm{3x}+\mathrm{7}}−\sqrt[{\mathrm{3}\:\:}]{\mathrm{20x}+\mathrm{4}}\:+{a}\mathrm{x}+{b}}{\left({x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\mathrm{exist}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{ab}\: \\ $$ Answered by i jagooll last updated on 29/May/20…
Question Number 30432 by abdo imad last updated on 22/Feb/18 $${find}\:\:{lim}_{{n}\rightarrow\infty\:} \sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{k}}{{n}}{e}^{−\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }} \:\:\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 30409 by abdo imad last updated on 22/Feb/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:{x}^{{i}+{j}} \:\:.{with}\:\mid{x}\mid<\mathrm{1}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161437 by cortano last updated on 17/Dec/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{10}}]{\mathrm{8}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}\:+\sqrt[{\mathrm{5}}]{\mathrm{7}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1}}−\mathrm{2}}{{x}}\:=? \\ $$ Answered by bobhans last updated on 18/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{10}}]{\mathrm{8x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{1}}−\mathrm{1}+\sqrt[{\mathrm{5}}]{\mathrm{7x}^{\mathrm{2}}…
Question Number 30366 by diyatrivedi last updated on 21/Feb/18 Commented by abdo imad last updated on 21/Feb/18 $${for}\:{x}\neq{a}\:\:\:\:\mid{sin}\left(\frac{\mathrm{1}}{{x}−{a}}\right)\mid\leqslant\mathrm{1}\:\Rightarrow\mid{x}−{a}\mid\mid{sin}\left(\frac{\mathrm{1}}{{x}−{a}}\right)\mid\leqslant\mid{x}−{a}\mid \\ $$$${but}\:\:{lim}_{{x}\rightarrow{a}} \mid{x}−{a}\mid=\mathrm{0}\:\Rightarrow\:{lim}_{{x}\rightarrow{a}} {f}\left({x}\right)=\mathrm{0}\:={f}\left(\mathrm{0}\right)\:{so}\:{f}\:{is} \\ $$$${continue}\:{at}\:{point}\:{x}_{\mathrm{0}} ={a}\:.…