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Question Number 91954 by john santu last updated on 04/May/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{sin}\:\mathrm{2x}\right)}{\mathrm{ln}\left(\mathrm{sin}\:\mathrm{4x}\right)} \\ $$ Commented by jagoll last updated on 04/May/20 $$\mathrm{doesn}'\mathrm{t}\:\mathrm{exist} \\ $$…
Question Number 26402 by abdo imad last updated on 25/Dec/17 $${find}\:{the}\:{nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \frac{{n}!}{\mathrm{1}+\mathrm{2}^{{n}} }\:\:. \\ $$ Commented by prakash jain last updated on 25/Dec/17 $${n}!=\mathrm{2}^{{n}−\mathrm{1}}…
Question Number 26401 by abdo imad last updated on 25/Dec/17 $${find}\:{the}\:{sum}\:{of}\:\: \\ $$$$\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}\:\:\mathrm{2}^{{n}} }\:\:. \\ $$ Commented by abdo imad last updated on…
Question Number 91897 by john santu last updated on 03/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{2}{x}−\mathrm{sin}\:{x}\right)}{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:=\:? \\ $$ Commented by john santu last updated on 03/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{x}−\mathrm{sin}\:{x}}{\mathrm{1}−\left(\mathrm{1}−\frac{{x}^{\mathrm{2}}…
Question Number 157389 by cortano last updated on 22/Oct/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{6}{e}^{{x}^{\mathrm{2}} } −\mathrm{20ln}\:\mid{x}\mid}{\mathrm{6}{e}^{{x}^{\mathrm{2}} } −\mathrm{20ln}\:\mid{x}\mid+\mathrm{3}}\right)^{\mathrm{3}{e}^{\mathrm{2}{x}^{\mathrm{2}} } \:\mathrm{sin}\:\left(\frac{\mathrm{6}{k}}{{e}^{{x}^{\mathrm{2}} } }\right)} =\mathrm{26} \\ $$$$\:{k}=? \\ $$$$ \\…
Question Number 26294 by d.monhbayr@gmail.com last updated on 23/Dec/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+{x}\mathrm{sin}\:{x}\:}−\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}{{tg}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}} \\ $$ Commented by abdo imad last updated on 24/Dec/17 $${for}\:{x}\in{v}\left(\mathrm{0}\right)\:\:\sqrt{\mathrm{1}+{u}}\sim\mathrm{1}+\frac{{u}\:}{\mathrm{2}} \\ $$$${tanu}\sim{u}…
Question Number 26293 by d.monhbayr@gmail.com last updated on 23/Dec/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{3}\sqrt{\left.\mathrm{1}−{x}^{\mathrm{3}} +{x}\right)}\right. \\ $$ Answered by Joel578 last updated on 24/Dec/17 $${L}\:=\:\mathrm{3}\:.\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{1}\:+\:{x}\:−\:{x}^{\mathrm{3}} } \\…
Question Number 26289 by d.monhbayr@gmail.com last updated on 23/Dec/17 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{x}−\mathrm{2}}−\frac{\mathrm{12}}{{x}^{\mathrm{3}} −\mathrm{8}}\right) \\ $$ Answered by prakash jain last updated on 24/Dec/17 $$\frac{\mathrm{1}}{{x}−\mathrm{2}}−\frac{\mathrm{1}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)} \\…
Question Number 91813 by jagoll last updated on 03/May/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−{x}+\:\mathrm{ln}\:{x}}{\mathrm{1}−\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} }}\:? \\ $$ Commented by john santu last updated on 03/May/20 $${L}'{Hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{1}}…