Question Number 119977 by bramlexs22 last updated on 28/Oct/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{4}} }\left(\sqrt[{\mathrm{5}}]{{x}+\mathrm{1}}−\sqrt[{\mathrm{5}}]{{x}}\:\right)\right)=? \\ $$ Answered by bemath last updated on 28/Oct/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}} +{x}^{\mathrm{4}} }−\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}}…
Question Number 185510 by mathlove last updated on 23/Jan/23 Answered by mahdipoor last updated on 23/Jan/23 $$\mathrm{6}{x}−\mathrm{8}{sin}\left({x}\right)+{sin}\left(\mathrm{2}{x}\right)= \\ $$$$\mathrm{6}{x}−\mathrm{8}\left({x}−\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}+\frac{{x}^{\mathrm{5}} }{\mathrm{5}!}−\frac{{x}^{\mathrm{7}} }{\mathrm{7}!}+….\right)+ \\ $$$$\left(\mathrm{2}{x}−\frac{\mathrm{8}{x}^{\mathrm{3}} }{\mathrm{3}!}+\frac{\mathrm{32}{x}^{\mathrm{5}}…
Question Number 119961 by bobhans last updated on 28/Oct/20 $${Without}\:{L}'{Hopital}\:{rule}\: \\ $$$$\:\underset{{x}\rightarrow\pi/\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{3}}\right)}{\mathrm{1}−\mathrm{2cos}\:{x}}\:? \\ $$ Answered by bramlexs22 last updated on 28/Oct/20 Answered by Dwaipayan…
Question Number 54409 by pooja24 last updated on 03/Feb/19 $${li}\underset{{x}\rightarrow\infty} {{m}}\sqrt{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)}−{x}=? \\ $$$${pls}\:{solve}\:{this} \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated…
Question Number 119902 by benjo_mathlover last updated on 28/Oct/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} {x}}} \:? \\ $$ Answered by benjo_mathlover last updated on 28/Oct/20 Answered by Olaf…
Question Number 185438 by mathlove last updated on 21/Jan/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{a}^{{x}} \mathrm{sin}\:\left({ax}\right)−{b}^{{x}} \mathrm{sin}\:\left({bx}\right)}{\left.{c}^{{x}} \mathrm{sin}\:\left({cx}\right)−{d}^{{x}} \mathrm{sin}\:{dx}\right)}=\:? \\ $$ Answered by hmr last updated on 21/Jan/23 $${L}'\:{Hopital}\:{Rule}:…
Question Number 54341 by Meritguide1234 last updated on 02/Feb/19 Answered by iv@0uja last updated on 03/Feb/19 $$\underset{{t}=\mathrm{0}} {\overset{{s}} {\sum}}\:_{{s}} {C}_{{t}} \left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)^{{t}} =\left(\mathrm{1}+\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)^{{s}} =\left(\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}\right)^{{s}} \\ $$$$\underset{{s}=\mathrm{0}}…
Question Number 185405 by greougoury555 last updated on 21/Jan/23 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({x}+\mathrm{2}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }{\left({x}+\mathrm{3}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }\:=? \\ $$ Answered by Frix last updated on 22/Jan/23 $$=\underset{{t}\rightarrow\mathrm{0}^{+}…
Question Number 185406 by greougoury555 last updated on 21/Jan/23 $${If}\:{a},{b},{c}\:{and}\:{d}\:{are}\:{constants}\:{such}\:{that} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{ax}^{\mathrm{2}} +\mathrm{sin}\:{bx}+\mathrm{sin}\:{cx}+\mathrm{sin}\:{dx}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{7}{x}^{\mathrm{6}} }=\mathrm{8} \\ $$$${find}\:{the}\:{value}\:{of}\:{the}\:{sum}\:{a}+{b}+{c}+{d} \\ $$ Answered by witcher3 last…
Question Number 119867 by Study last updated on 27/Oct/20 $${li}\underset{{x}\rightarrow\infty} {{m}}\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{n}}\right)^{{n}} −\sqrt{{e}}}{\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)^{{n}} −{e}^{\mathrm{2}} }=??? \\ $$ Commented by Dwaipayan Shikari last updated on 27/Oct/20 $$\frac{\mathrm{1}}{\mathrm{16}}{e}^{−\frac{\mathrm{3}}{\mathrm{2}}}…