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 \\ $$$${but}\:\:{lim}_{{x}\rightarrow{a}} \mid{x}−{a}\mid=\mathrm{0}\:\Rightarrow\:{lim}_{{x}\rightarrow{a}} {f}\left({x}\right)=\mathrm{0}\:={f}\left(\mathrm{0}\right)\:{so}\:{f}\:{is} \\ $$$${continue}\:{at}\:{point}\:{x}_{\mathrm{0}} ={a}\:.…
Question Number 161386 by savitar last updated on 17/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 95832 by M±th+et+s last updated on 28/May/20 $${find}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{{e}^{\mathrm{2}−{x}} −\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 161361 by cortano last updated on 17/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}+\mathrm{1}}\:+\sqrt[{{h}}]{\mathrm{1}+\mathrm{2}{x}}−\mathrm{2}}{{x}}\:=\:\frac{\mathrm{3}}{\mathrm{5}}\: \\ $$$$\:\:{h}^{\mathrm{3}} −\frac{\mathrm{2}}{\mathrm{9}}\left({h}+\mathrm{7}\right)=? \\ $$ Commented by vietanhdz last updated on 17/Dec/21 $$\sqrt{{x}+\mathrm{1}}−\mathrm{1}\sim\frac{{x}}{\mathrm{2}}\:{if}\:{x}\sim\mathrm{0} \\…