Question Number 169147 by mathlove last updated on 25/Apr/22 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{2}{cosx}}{{sin}\left({x}−\frac{\pi}{\mathrm{3}}\right)}=? \\ $$ Commented by cortano1 last updated on 25/Apr/22 $$\:{let}\:{x}−\frac{\pi}{\mathrm{3}}={h} \\ $$$$\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{2cos}\:\left(\frac{\pi}{\mathrm{3}}+{h}\right)}{\mathrm{sin}\:{h}} \\…
Question Number 169052 by cortano1 last updated on 23/Apr/22 $$\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\frac{\mathrm{1}+\mathrm{2}{x}}{\mathrm{1}−\mathrm{3}{x}}}\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:\sqrt[{\mathrm{4}}]{\frac{\mathrm{1}+\mathrm{4}{x}}{\mathrm{1}+\mathrm{3}{x}}}\:−\mathrm{1}}{\mathrm{2}{x}}\:=? \\ $$ Commented by infinityaction last updated on 23/Apr/22 $$\frac{\mathrm{41}}{\mathrm{24}}??? \\ $$ Commented by…
Question Number 103463 by bemath last updated on 15/Jul/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{3}{e}^{\mathrm{2}{x}} +\mathrm{5}{e}^{{x}} −\mathrm{2}\right)}{\mathrm{ln}\left(\mathrm{27}{e}^{\mathrm{3}{x}} −\mathrm{1}\right)}\:? \\ $$ Answered by Worm_Tail last updated on 15/Jul/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{3}{e}^{\mathrm{2}{x}}…
Question Number 168964 by cortano1 last updated on 22/Apr/22 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{2}{t}}{\:\sqrt{\mathrm{4}+{t}^{\mathrm{2}} }\:\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\left(\sqrt{\mathrm{1}+{t}}−\mathrm{1}\right){dt}}\:{dt}\:=?\: \\ $$ Answered by greougoury555 last updated on 22/Apr/22…
Question Number 168966 by cortano1 last updated on 22/Apr/22 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\int_{\mathrm{0}} ^{\:{x}} \:\left(\int_{\mathrm{0}} ^{\:{u}^{\mathrm{2}} } \mathrm{tan}^{−\mathrm{1}} \left(\mathrm{1}+{t}\right){dt}\right){dt}\:}{{x}−{x}\:\mathrm{cos}\:{x}}\:=? \\ $$ Answered by bobhans last updated on…
Question Number 168911 by bagjagugum123 last updated on 21/Apr/22 Commented by infinityaction last updated on 21/Apr/22 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\frac{\left({x}^{\mathrm{2}} −{a}^{\mathrm{2}} \right)\mathrm{sin}\:\left({x}−{a}\right)\left(\sqrt{{x}+{b}}+\sqrt{{a}+{b}}\right)^{\mathrm{2}} }{\:\left(\sqrt{{x}+{b}}−\sqrt{{a}+{b}}\right)^{\mathrm{2}} \left(\sqrt{{x}+{b}}+\sqrt{{a}+{b}}\right)^{\mathrm{2}} } \\ $$$$\underset{{x}\rightarrow{a}}…
Question Number 103366 by Study last updated on 14/Jul/20 Answered by mathmax by abdo last updated on 14/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{4}}} −\mathrm{5}^{\frac{\mathrm{1}}{\left\{\right.}} }{\left(\mathrm{lnx}\right)^{\frac{\mathrm{1}}{\mathrm{8}}} −\left(\mathrm{ln5}\right)^{\frac{\mathrm{1}}{\mathrm{8}}} }\:\:\mathrm{let}\:\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{5}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement} \\…
Question Number 37816 by prof Abdo imad last updated on 17/Jun/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{ln}\left({x}+{e}^{{sinx}} \right)\:−{x}^{\mathrm{2}} }{{sh}\left(\mathrm{2}{x}\right)} \\ $$ Commented by math khazana by abdo last updated…
Question Number 103313 by gui last updated on 14/Jul/20 $${li}\underset{{n}\rightarrow+\infty} {{m}}\left(\mathrm{ln}\:\left({n}!\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 168819 by AbdoulayeLelouche last updated on 18/Apr/22 $$\mathrm{D}\acute {\mathrm{e}montrer}\:\mathrm{que}: \\ $$$$\mathrm{Demonstrate}\:\mathrm{that}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{e}^{{x}} −\mathrm{1}−\mathrm{ln}\:\left({x}+\mathrm{1}\right)}{\mathrm{cos}\:\left({x}\right)−\mathrm{1}}\right)\:=\:−\mathrm{2} \\ $$ Answered by alephzero last updated on…