Question Number 109139 by bemath last updated on 21/Aug/20 $$\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left(\mathrm{1}−{x}\right)\:\mathrm{sin}\:\mid\mathrm{2}{x}−\mathrm{2}\mid\:? \\ $$ Commented by kaivan.ahmadi last updated on 21/Aug/20 $${x}\rightarrow−\infty\Rightarrow\mathrm{2}{x}−\mathrm{2}\rightarrow−\infty\Rightarrow\mid\mathrm{2}{x}−\mathrm{2}\mid\rightarrow+\infty\Rightarrow \\ $$$$−\mathrm{1}\leqslant{sin}\mid\mathrm{2}{x}−\mathrm{2}\mid\leqslant\mathrm{1}\:{is}\:{an}\:{element}\:{of}\:{R}\:{we} \\ $$$${say}\:{a}.…
Question Number 174630 by infinityaction last updated on 06/Aug/22 $$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{r}}{{n}^{\mathrm{2}} +{r}} \\ $$ Answered by mnjuly1970 last updated on 06/Aug/22 $$\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \left\{\frac{\mathrm{1}}{\mathrm{1}+{n}^{\:\mathrm{2}}…
Question Number 109091 by bemath last updated on 21/Aug/20 $$\:\:\:\:\frac{\bigtriangleup\flat{e}\mathscr{M}{ath}\bigtriangledown}{\equiv\multimap\equiv\multimap\equiv} \\ $$$$\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{\:\sqrt{\pi+\mathrm{tan}\:{x}}−\sqrt{\pi−\mathrm{tan}\:{x}}}\:? \\ $$ Answered by bobhans last updated on 21/Aug/20 Commented by bobhans…
Question Number 109068 by n0y0n last updated on 20/Aug/20 Answered by Dwaipayan Shikari last updated on 20/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left({cos}\mathrm{5}{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{{x}^{\mathrm{4}} }} =\left(\mathrm{1}−\frac{\mathrm{25}{x}^{\mathrm{4}} }{\mathrm{2}}\right)^{\frac{−\mathrm{2}}{{x}^{\mathrm{4}} .\mathrm{25}}.\left(\frac{−\mathrm{25}}{\mathrm{2}}\right)} ={e}^{−\frac{\mathrm{25}}{\mathrm{2}}}…
Question Number 109067 by n0y0n last updated on 20/Aug/20 Answered by Aziztisffola last updated on 20/Aug/20 $$\:\mathrm{sin}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{cot}^{\mathrm{2}} \left(\mathrm{x}\right)\right)=\mathrm{sin}\left(\mathrm{x}\right)\mathrm{ln}\left(\frac{\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}\right) \\ $$$$\:=\mathrm{sin}\left(\mathrm{x}\right)\left(\mathrm{ln}\left(\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)\right)−\mathrm{sin}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\right)\right. \\…
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Question Number 108997 by 150505R last updated on 20/Aug/20 Answered by Dwaipayan Shikari last updated on 20/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{sin}\left({n}^{\mathrm{2}} \pi\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{3}}{{n}}+\frac{\mathrm{4}}{{n}^{\mathrm{2}} }−\frac{\mathrm{5}}{{n}^{\mathrm{3}} }}\:\right) \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{sin}\left({n}^{\mathrm{2}}…
Question Number 108956 by bobhans last updated on 20/Aug/20 $$\:\:\:\:\:\:\:\:\:\overset{\bigstar} {{b}}\overset{\bigstar} {{o}}\overset{\bigstar} {{b}}\overset{\Box} {{h}}\overset{\Box} {{a}}\overset{\Box} {{n}}\overset{\spadesuit} {{s}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{8}{x}−\mathrm{sin}\:\mathrm{4}{x}.\mathrm{cos}\:\mathrm{4}{x}}{{x}.\mathrm{sin}\:\mathrm{4}{x}.\mathrm{tan}\:\mathrm{8}{x}}\:? \\ $$ Answered by john…
Question Number 174407 by infinityaction last updated on 31/Jul/22 $$\:{evaluate} \\ $$$$\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{3}^{\mathrm{sin}{x}\:} +\mathrm{2}{x}\:+\mathrm{1}}{\mathrm{sin}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:} \\ $$ Answered by CElcedricjunior last updated on 31/Jul/22 $$\underset{{x}\rightarrow−\infty}…