Question Number 200873 by cortano12 last updated on 25/Nov/23 Commented by witcher3 last updated on 26/Nov/23 $$\mathrm{tan}\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)\in\left[−\sqrt{\mathrm{3}},\sqrt{\mathrm{3}}\right] \\ $$$$\mathrm{tg}\left(\mathrm{3}.\frac{\mathrm{x}}{\mathrm{2}}\right)=\frac{\mathrm{3tg}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\mathrm{tg}^{\mathrm{3}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)}{\mathrm{1}−\mathrm{3tg}^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)} \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\sqrt{\mathrm{3}−\mathrm{tan}^{\mathrm{2}} \left(\frac{\mathrm{3x}}{\mathrm{2}}\right)}=\mathrm{2}+\mathrm{cos}\left(\mathrm{x}\right) \\…
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Question Number 200864 by Rydel last updated on 25/Nov/23 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{xE}\left({x}\right)+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{sin}\:{x}}} \\ $$ Answered by Mathspace last updated on 25/Nov/23 $$={lim}_{{x}\rightarrow+\infty} \frac{{xE}\left({x}\right)+\mathrm{3}}{{x}\sqrt{\mathrm{1}+\frac{{sinx}}{{x}^{\mathrm{2}} }}} \\…
Question Number 200844 by darklord last updated on 24/Nov/23 Commented by som(math1967) last updated on 24/Nov/23 $$?? \\ $$ Commented by darklord last updated on…
Question Number 200831 by cortano12 last updated on 24/Nov/23 Commented by mathfreak01 last updated on 24/Nov/23 $$ \\ $$not enough data Terms of Service Privacy…
Question Number 200856 by sonukgindia last updated on 24/Nov/23 Commented by mr W last updated on 24/Nov/23 $${R}=\mathrm{1}\:{cm}\:={bigger}\:{radius} \\ $$$${r}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:{cm}\:={smaller}\:{radius} \\ $$$${yellow}\:{area}={R}×{r}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:{cm}^{\mathrm{2}} \\ $$ Terms…
Question Number 200840 by Rydel last updated on 24/Nov/23 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{x}^{{n}} \mathrm{sin}\:{a}−{a}^{{n}} \mathrm{sin}\:{x}}{{x}−{a}} \\ $$ Answered by MM42 last updated on 24/Nov/23 $${lim}_{{x}\rightarrow{a}} \:\frac{{x}^{{n}} {sina}−{a}^{{n}}…
Question Number 200836 by Rasheed.Sindhi last updated on 24/Nov/23 $$ \\ $$$$\mathcal{L}{et}\overline {\:{abc}\:}+\overline {\:{bca}\:}+\overline {\:{cab}\:}=\overline {\:{defg}\:} \\ $$$${where}\:{a},{b},…,{g}\:{are}\:{decimal}\:{digits} \\ $$$$\left({may}\:{be}\:{equal}\:{to}\:\mathrm{0}\right)\: \\ $$$${Show}\:{that} \\ $$$$\left({i}\right)\overline {\:{dg}\:}={a}+{b}+{c}…
Question Number 200821 by Calculusboy last updated on 24/Nov/23 Answered by shunmisaki007 last updated on 24/Nov/23 $$\mathrm{ln}\left(\mathrm{10}!\right) \\ $$$$=\mathrm{ln}\left(\mathrm{10}\centerdot\mathrm{9}\centerdot\mathrm{8}\centerdot\mathrm{7}\centerdot\mathrm{6}\centerdot\mathrm{5}\centerdot\mathrm{4}\centerdot\mathrm{3}\centerdot\mathrm{2}\centerdot\mathrm{1}\right) \\ $$$$=\mathrm{ln}\left(\left(\mathrm{2}\centerdot\mathrm{5}\right)\centerdot\mathrm{3}^{\mathrm{2}} \centerdot\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{7}\centerdot\left(\mathrm{2}\centerdot\mathrm{3}\right)\centerdot\mathrm{5}\centerdot\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}\centerdot\mathrm{2}\centerdot\mathrm{1}\right) \\…