Question Number 83710 by john santu last updated on 05/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}} }{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} }\:=\:? \\ $$ Commented by john santu last updated on…
Question Number 149251 by john_santu last updated on 04/Aug/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{tan}\:\mathrm{x}}−\mathrm{sin}\:\mathrm{x}\:\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} \:\sqrt{\mathrm{x}}}\:=? \\ $$$$ \\ $$ Answered by dumitrel last updated on 04/Aug/21 $$\underset{{x}\rightarrow\mathrm{0}^{+}…
Question Number 149239 by john_santu last updated on 04/Aug/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{a}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}}−\sqrt{\mathrm{a}}\:−\sqrt{\mathrm{x}−\mathrm{a}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}\:=?\: \\ $$ Answered by EDWIN88 last updated on 04/Aug/21 $$\:\underset{{x}\rightarrow{a}^{+} }…
Question Number 83690 by jagoll last updated on 05/Mar/20 $$\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\frac{\pi{x}+\mathrm{1}}{\mathrm{2}{x}+\mathrm{2}}\right)}{{x}+\mathrm{1}}\:=\:? \\ $$ Commented by mathmax by abdo last updated on 05/Mar/20 $${let}\:{f}\left({x}\right)=\frac{{tan}\left(\frac{\pi{x}+\mathrm{1}}{\mathrm{2}{x}+\mathrm{2}}\right)}{{x}+\mathrm{1}}\:\Rightarrow{f}\left({x}\right)=\frac{{tan}\left(\frac{\pi}{\mathrm{2}}×\frac{{x}+\frac{\mathrm{1}}{\pi}}{{x}+\mathrm{1}}\right)}{{x}+\mathrm{1}} \\ $$$$=\frac{{tan}\left(\frac{\pi}{\mathrm{2}}×\left(\frac{{x}+\mathrm{1}\:+\frac{\mathrm{1}}{\pi}−\mathrm{1}}{{x}+\mathrm{1}}\right)\right)}{{x}+\mathrm{1}}\:=\frac{{tan}\left(\frac{\pi}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}−\pi}{\pi\left({x}+\mathrm{1}\right)}\right)\right.}{{x}+\mathrm{1}}…
Question Number 83668 by jagoll last updated on 05/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}−{x}}{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\mathrm{2}{x}\right)}\:=\: \\ $$ Answered by john santu last updated on 05/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{sin}\:\left(\mathrm{2}{x}\right)−{x}}{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\mathrm{2}{x}\right)}\:=\:…
Question Number 149184 by liberty last updated on 03/Aug/21 $$\:\:\:\Omega\:=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{tan}\:\sqrt{\mathrm{3x}+\mathrm{2}}−\mathrm{tan}\:\sqrt{\mathrm{2x}+\mathrm{3}}}{\mathrm{tan}\:\sqrt{\mathrm{5x}+\mathrm{4}}−\mathrm{tan}\:\sqrt{\mathrm{4x}+\mathrm{5}}}\:=? \\ $$ Answered by EDWIN88 last updated on 03/Aug/21 $$\Omega=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\frac{\mathrm{3}}{\mathrm{2}\sqrt{\mathrm{3}{x}+\mathrm{2}}}\:\mathrm{sec}\:^{\mathrm{2}} \:\sqrt{\mathrm{3}{x}+\mathrm{2}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{x}+\mathrm{3}}}\mathrm{sec}\:^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{3}}}{\frac{\mathrm{5}}{\mathrm{2}\sqrt{\mathrm{5}{x}+\mathrm{4}}}\mathrm{sec}\:^{\mathrm{2}} \sqrt{\mathrm{5}{x}+\mathrm{4}}−\frac{\mathrm{2}}{\:\sqrt{\mathrm{4}{x}+\mathrm{5}}}\mathrm{sec}\:^{\mathrm{2}}…
Question Number 83587 by jagoll last updated on 04/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3sin}\:\pi\mathrm{x}−\mathrm{sin}\:\mathrm{3}\pi\mathrm{x}}{\mathrm{x}^{\mathrm{3}} } \\ $$ Commented by john santu last updated on 04/Mar/20 $$\mathrm{let}\:\mathrm{u}\:=\:\pi\mathrm{x}\:\Rightarrow\:\mathrm{x}=\:\frac{\mathrm{u}}{\pi} \\ $$$$\underset{\mathrm{u}\rightarrow\mathrm{0}}…
Question Number 83492 by jagoll last updated on 03/Mar/20 $$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}}} \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{f}\left(\mathrm{2x}−\mathrm{t}\right)+\mathrm{f}\left(\mathrm{2x}−\mathrm{2t}\right)−\mathrm{2f}\left(\mathrm{2x}+\mathrm{t}\right)}{\mathrm{t}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83493 by jagoll last updated on 03/Mar/20 $$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mid\mathrm{x}+\mathrm{p}\mid^{\mathrm{2}} −\mid\mathrm{2p}\mid^{\mathrm{2}} }{\mathrm{p}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }\:=\:\mathrm{L} \\ $$$$\mathrm{find}\:\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mid\mathrm{2p}\mid^{\mathrm{3}} −\mid\mathrm{x}+\mathrm{p}\mid^{\mathrm{3}} }{\mathrm{x}−\mathrm{p}} \\ $$ Terms of Service…
Question Number 17957 by Arnab Maiti last updated on 13/Jul/17 $$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{1}+\frac{\mathrm{a}}{\mathrm{x}}\right)^{\mathrm{n}} =\left(\mathrm{1}+\frac{\mathrm{an}}{\mathrm{x}}\right)\:,\:\:\mathrm{x}\gg\mathrm{a} \\ $$ Answered by 42 last updated on 13/Jul/17 $$\mathrm{Expand}\:\mathrm{using}\:\mathrm{binomial}\:\mathrm{theorem}: \\ $$$$\mathrm{1}\:+\:{n}\left(\frac{{a}}{{x}}\right)\:+\:\frac{{n}\left({n}\:−\:\mathrm{1}\right)}{\mathrm{2}}\left(\frac{{a}}{{x}}\right)^{\mathrm{2}} \:+\:……