Question Number 34843 by rahul 19 last updated on 11/May/18 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}_{} }\:\frac{\mathrm{ln}\:{x}}{{x}}\:=\:? \\ $$$${You}\:{can}\:\:{only}\:{use} \\ $$$${series}\:{expansion}\:/\:{sandwich}\:{theorem}! \\ $$ Commented by abdo mathsup 649 cc…
Question Number 100343 by student work last updated on 26/Jun/20 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{l}im}\:\frac{\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} }{\mathrm{f}\left(\mathrm{1}\right)}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{f}\left(\mathrm{1}\right)=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$ Commented by student work last updated on 26/Jun/20…
Question Number 165868 by cortano1 last updated on 09/Feb/22 $$\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}−\sqrt[{\mathrm{3}}]{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}}\:=? \\ $$ Answered by qaz last updated on 10/Feb/22 $$\underset{\mathrm{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}−\sqrt[{\mathrm{3}}]{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}} \\ $$$$=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}}…
Question Number 34755 by Joel579 last updated on 10/May/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{\mathrm{ln}^{\mathrm{1000}} \:\left(\mathrm{1}\:+\:{x}\right)}{{x}^{\mathrm{1001}} }\right) \\ $$ Commented by Joel579 last updated on 10/May/18 $${L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}\left(\mathrm{1}\:−\:\frac{\mathrm{ln}^{\mathrm{1000}} \:\left(\mathrm{1}\:+\:{x}\right)}{{x}^{\mathrm{1000}}…
Question Number 100289 by Ar Brandon last updated on 26/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{n}} {\overset{\mathrm{2n}} {\sum}}\mathrm{sin}\left(\frac{\pi}{\mathrm{k}}\right) \\ $$$${Riemann}'{s}\:{integral}\:{may}\:{help} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34737 by chakraborty ankit last updated on 10/May/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34694 by math khazana by abdo last updated on 09/May/18 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\sum_{{k}={n}} ^{\mathrm{2}{n}−\mathrm{1}} \:\:\frac{\mathrm{1}}{\mathrm{2}{k}+\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34681 by math khazana by abdo last updated on 09/May/18 $${calculate}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\left\{\:\frac{\mathrm{1}+{tanx}}{\mathrm{1}+{thx}}\right\}^{\frac{\mathrm{1}}{{sinx}}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 100134 by bemath last updated on 25/Jun/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{4sin}\:\mathrm{x}−\sqrt{\mathrm{6}\sqrt{\mathrm{sin}\:\mathrm{x}}+\mathrm{10}}}{\frac{\pi}{\mathrm{2}}−\mathrm{x}}\:? \\ $$ Commented by bobhans last updated on 25/Jun/20 $$\mathrm{set}\:\frac{\pi}{\mathrm{2}}−\mathrm{x}\:=\:\mathrm{t}\:,\:\mathrm{x}\:=\frac{\pi}{\mathrm{2}}−\mathrm{t}\: \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4cos}\:\mathrm{t}−\sqrt{\mathrm{6}\sqrt{\mathrm{cos}\:\mathrm{t}}+\mathrm{10}}}{\mathrm{t}}\:= \\…
Question Number 34554 by rahul 19 last updated on 07/May/18 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{a}−\mathrm{1}+{b}^{\frac{\mathrm{1}}{{x}}} }{{a}}\right)^{{x}} =\:? \\ $$$$\left({a},{b}>\mathrm{0}\right) \\ $$ Commented by math khazana by abdo last…