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Category: Limits

e-Math-lim-x-81x-2-10x-1-4x-3-25x-2-10x-1-

Question Number 109929 by bemath last updated on 26/Aug/20 $$\:\:\:\bigtriangleup\frac{\flat{e}}{\mathcal{M}{ath}}\bigtriangledown \\ $$$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{81}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{1}}−\mathrm{4}{x}+\mathrm{3}−\sqrt{\mathrm{25}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{1}}\:=? \\ $$ Commented by bemath last updated on 26/Aug/20 Terms…

JS-lim-x-3-5-2x-x-2-x-4-x-2-

Question Number 109861 by john santu last updated on 26/Aug/20 $$\:\:\frac{{JS}}{\blacksquare\bigstar\bigstar\blacksquare} \\ $$$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{5}−\mathrm{2}{x}+\sqrt{{x}−\mathrm{2}}}{{x}−\mathrm{4}+\sqrt{{x}−\mathrm{2}}}\:? \\ $$ Answered by bemath last updated on 26/Aug/20 Commented by…

lim-x-pi-4-sin-x-cos-x-tan-pi-8-x-2-

Question Number 175362 by cortano1 last updated on 28/Aug/22 $$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{\mathrm{tan}\:\left(\frac{\pi}{\mathrm{8}}−\frac{{x}}{\mathrm{2}}\right)}\:=? \\ $$ Commented by infinityaction last updated on 28/Aug/22 $$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{−\sqrt{\mathrm{2}}\mathrm{sin}\left(\pi/\mathrm{4}−{x}\right)}{\mathrm{sin}\left(\frac{\pi}{\mathrm{8}}−\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\:\left(\frac{\pi}{\mathrm{8}}−\frac{{x}}{\mathrm{2}}\right)\:\:} \\ $$$$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{−\mathrm{2}\sqrt{\mathrm{2}}\cancel{\mathrm{sin}\left(\frac{\pi}{\mathrm{8}}−\frac{{x}}{\mathrm{2}}\right)}\mathrm{cos}\left(\frac{\pi}{\mathrm{8}}−\frac{{x}}{\mathrm{2}}\right)\:\:}{\cancel{\mathrm{sin}\left(\frac{\pi}{\mathrm{8}}−\frac{{x}}{\mathrm{2}}\right)}}…

lim-x-1-cos-xcos-2xcos-3x-1-cos-x-

Question Number 109769 by Karani last updated on 25/Aug/20 $$\underset{{x}\rightarrow\Pi} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{3}{x}}{\mathrm{1}−\mathrm{cos}\:{x}}=? \\ $$ Answered by bemath last updated on 25/Aug/20 $$\:\:\:\bigtriangleup\frac{\flat\epsilon}{{math}}\bigtriangledown \\ $$$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\pi.\mathrm{cos}\:\mathrm{2}\pi.\mathrm{cos}\:\mathrm{3}\pi}{\mathrm{1}−\mathrm{cos}\:\pi}\:=\:\frac{\mathrm{1}−\left(−\mathrm{1}\right)\left(\mathrm{1}\right)\left(−\mathrm{1}\right)}{\mathrm{2}}=\mathrm{0} \\…

lim-n-3-1-n-8-5-1-n-32-

Question Number 109763 by Karani last updated on 25/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{3}}{\mathrm{1}−^{{n}} \sqrt{\mathrm{8}}}−\frac{\mathrm{5}}{\mathrm{1}−^{{n}} \sqrt{\mathrm{32}}}\right)=? \\ $$ Answered by bemath last updated on 25/Aug/20 $$\:\:\:\bigtriangledown\frac{\flat{e}}{{math}}\Delta \\ $$$$\underset{{n}\rightarrow\infty}…