Question Number 161133 by qaz last updated on 12/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{n}}\right)}=? \\ $$ Answered by ArielVyny last updated on 12/Dec/21 $$\frac{\mathrm{1}}{{n}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{{x}\left({x}+\frac{\mathrm{1}}{{n}}\right)}=\int_{\mathrm{0}}…
Question Number 161111 by cortano last updated on 12/Dec/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} +\mathrm{2cos}\:{x}−\mathrm{2}}{{x}^{\mathrm{4}} }\:=\:\frac{\mathrm{1}}{{a}} \\ $$$$\:\:\:\:{a}=? \\ $$ Commented by blackmamba last updated on 12/Dec/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 29974 by hanieert last updated on 14/Feb/18 $$\sqrt{\mathrm{5}=?} \\ $$ Answered by MJS last updated on 14/Feb/18 $$ \\ $$$$\mathrm{2}.\mathrm{2360679774}… \\ $$ Terms…
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Question Number 161002 by bobhans last updated on 10/Dec/21 $$\:\:\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ax}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{2x}}\:\sqrt{\mathrm{1}+\mathrm{bx}}\:−\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\mathrm{then}\:\mathrm{a}×\mathrm{b}\:=? \\ $$ Answered by blackmamba last updated on 11/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{ax}}{\left(\mathrm{1}+\frac{\mathrm{2}{x}}{\mathrm{3}}\right)\left(\mathrm{1}+\frac{{bx}}{\mathrm{2}}\right)−\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\…
Question Number 160995 by bobhans last updated on 10/Dec/21 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{sin}\:\mathrm{2x}−\mathrm{2tan}\:\mathrm{x}\right)^{\mathrm{2}} +\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2x}\right)^{\mathrm{3}} }{\mathrm{tan}\:^{\mathrm{7}} \mathrm{6x}\:+\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}}=? \\ $$ Commented by blackmamba last updated on 11/Dec/21 $$\:\:\left(\bullet\right)\left(\mathrm{sin}\:\mathrm{2}{x}−\mathrm{2tan}\:{x}\right)^{\mathrm{2}}…
Question Number 29875 by tawa tawa last updated on 13/Feb/18 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{or}\:\mathrm{divergent}\:\mathrm{of}\:\:\:\:\:\:\:\:\:\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\right)_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160937 by blackmamba last updated on 09/Dec/21 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\:\mathrm{sin}\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:\right)=? \\ $$ Answered by aleks041103 last updated on 14/Dec/21 $${sin}\left({a}\right)−{sin}\left({b}\right)= \\ $$$$={sin}\left(\frac{{a}+{b}}{\mathrm{2}}+\frac{{a}−{b}}{\mathrm{2}}\right)−{sin}\left(\frac{{a}+{b}}{\mathrm{2}}−\frac{{a}−{b}}{\mathrm{2}}\right)=…
Question Number 95401 by john santu last updated on 25/May/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}^{\frac{\mathrm{3}}{\mathrm{2}}} \left\{\sqrt{\mathrm{n}+\mathrm{1}}+\sqrt{\mathrm{n}−\mathrm{1}}−\mathrm{2}\sqrt{\mathrm{n}}\:\right\}\: \\ $$ Answered by john santu last updated on 25/May/20 Commented by…
Question Number 160938 by cortano last updated on 09/Dec/21 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left(\frac{\pi}{\mathrm{cos}\:\mathrm{x}}\:−\mathrm{2x}\:\mathrm{tan}\:\mathrm{x}\:\right)=? \\ $$ Answered by blackmamba last updated on 09/Dec/21 Terms of Service Privacy Policy…