Question Number 170547 by qaz last updated on 26/May/22 $$\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{x}}\int_{\mathrm{x}} ^{\mathrm{x}+\mathrm{1}} \frac{\mathrm{sin}\:\mathrm{t}}{\:\sqrt{\mathrm{t}+\mathrm{cos}\:\mathrm{t}}}\mathrm{dt}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 170537 by 2407 last updated on 26/May/22 Commented by cortano1 last updated on 26/May/22 $$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{{n}}\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{n}}}}\:−\sqrt{{n}}\:= \\ $$$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{{n}}\:\left(\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{n}}}}\:−\mathrm{1}\right)= \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$…
Question Number 104899 by bramlex last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)−\mathrm{cos}\:\left({x}\right)}{{x}^{\mathrm{4}} }\:?\: \\ $$ Answered by john santu last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−\mathrm{2sin}\:\left(\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{2}}\right)\mathrm{sin}\:\left(\frac{\mathrm{sin}\:{x}−{x}}{\mathrm{2}}\right)}{{x}^{\mathrm{4}} }…
Question Number 104850 by ~blr237~ last updated on 24/Jul/20 $${Let}\:\:{E}\:{be}\:{a}\:{no}\:{empty}\:{set}\:{with}\:{card}={n}\geqslant\mathrm{1} \\ $$$$\:{Find}\:{in}\:{term}\:{of}\:\:{n}\:\:\:\:\:\:\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}−{B}\right)=\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}\cap{B}\right)=\frac{\mathrm{1}}{\mathrm{3}}\underset{{A},{B}\subseteq{E}} {\sum}{Card}\:\left({A}\cup{B}\right)={n}\mathrm{4}^{{n}−\mathrm{1}} \:\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104838 by bramlex last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\:^{\mathrm{3}} \left(\mathrm{8}{x}\right)−\mathrm{1}}{\mathrm{6}{x}^{\mathrm{2}} }\:? \\ $$ Answered by john santu last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{8}{x}−\mathrm{1}\right)\left(\mathrm{cos}\:^{\mathrm{2}}…
Question Number 104812 by bobhans last updated on 24/Jul/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\frac{\mathrm{3}}{{x}}\right)}{\left(\frac{\mathrm{2}}{{x}}+\mathrm{5}\right)^{\mathrm{2}} −\mathrm{25}}\:? \\ $$ Answered by bemath last updated on 24/Jul/20 $${set}\:\frac{\mathrm{1}}{{x}}\:=\:{a}\:,\:{a}\rightarrow\mathrm{0} \\ $$$$\underset{{a}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3}{a}}{\left(\mathrm{2}{a}+\mathrm{5}\right)^{\mathrm{2}}…
Question Number 170321 by amin96 last updated on 20/May/22 Answered by aleks041103 last updated on 21/May/22 $$\left.{a}\right) \\ $$$$\frac{\mathrm{2}^{{x}} }{\mathrm{3}^{{x}^{\mathrm{2}} } }=\mathrm{2}^{{x}} \mathrm{3}^{−{x}^{\mathrm{2}} } ={e}^{{ln}\left(\mathrm{2}\right){x}−{ln}\left(\mathrm{3}\right){x}^{\mathrm{2}}…
Question Number 170318 by amin96 last updated on 20/May/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104746 by bobhans last updated on 23/Jul/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{3}{x}} +\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{x}} \right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \: \\ $$ Answered by Dwaipayan Shikari last updated on 23/Jul/20…
Question Number 170221 by mathlove last updated on 18/May/22 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\left(\frac{\left(\sqrt{{x}}\right)^{\sqrt{{x}}} −{x}^{{x}} }{\left(\sqrt{{x}}\right)^{{x}} −{x}^{\sqrt{{x}}} }\right)=? \\ $$$${help}\:{me} \\ $$ Commented by mathlove last updated…