Question Number 199662 by cortano12 last updated on 07/Nov/23 $$ \\ $$$$\mathrm{A}\:\mathrm{point}\:\mathrm{moves}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{5}}\:\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{it}'\mathrm{s}\:\mathrm{x}−\mathrm{coordinate}\:\mathrm{increases}\: \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{3}\sqrt{\mathrm{10}}\:\:\mathrm{cm}/\mathrm{s}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{it}'\mathrm{s} \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{0}\right) \\ $$$$\mathrm{when}\:\mathrm{x}\:=\:\mathrm{2}…
Question Number 199597 by mnjuly1970 last updated on 05/Nov/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{Q}\::\:\:\:\:\:\:\mathrm{lim}_{\:{x}\rightarrow\:\frac{\pi}{\mathrm{4}}} \:\:\left(\:\:\mathrm{1}\:+\:\:{sin}\left({x}\right)\:−{cos}\left({x}\right)\:\right)^{\:{tan}\left(\mathrm{2}{x}\right)} \:=\:\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet\:\mathscr{N}{ice}\:−\:\mathscr{M}{athematics}\:\bullet\: \\ $$$$\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 199553 by cortano12 last updated on 05/Nov/23 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)}{\mathrm{x}^{\mathrm{2}} \:\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{2}}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{2}}\:\right)}\:=? \\ $$ Answered by MM42 last updated on 05/Nov/23 $$−\frac{\sqrt{\mathrm{2}}}{\mathrm{8}}\:{i}\:\:\checkmark \\…
Question Number 199467 by Calculusboy last updated on 04/Nov/23 Answered by cortano12 last updated on 04/Nov/23 $$\:\mathrm{4}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{a}−\mathrm{2}\right)\mathrm{x}^{\mathrm{3}} +\left(\mathrm{3}+\mathrm{c}\right)\mathrm{x}^{\mathrm{2}} +\left(\mathrm{b}−\mathrm{3}\right)\mathrm{x}+\mathrm{2}+\mathrm{d}}{\mathrm{x}^{\mathrm{2}} \:\left[\sqrt{\mathrm{1}+\frac{\mathrm{a}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{3}} }+\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{4}} }}\:+\sqrt{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}}−\frac{\mathrm{c}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{3}}…
Question Number 199370 by mathlove last updated on 02/Nov/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}{e}^{\mathrm{3}{x}} −\mathrm{9}{e}^{\mathrm{2}{x}} +\mathrm{6}{x}+\mathrm{5}}{{x}^{\mathrm{3}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 199393 by Calculusboy last updated on 02/Nov/23 Answered by cortano12 last updated on 03/Nov/23 $$\:\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\frac{\mathrm{x}}{\mathrm{2011}}\right)\left(\mathrm{1}+\frac{\mathrm{2x}}{\mathrm{2012}}\right)\left(\mathrm{1}+\frac{\mathrm{3x}}{\mathrm{2013}}\right)−\mathrm{1}}{\mathrm{x}} \\ $$$$\:\:\mathrm{A}=\:\frac{\mathrm{1}}{\mathrm{2011}}\:+\frac{\mathrm{2}}{\mathrm{2012}}\:+\:\frac{\mathrm{3}}{\mathrm{2013}}\: \\ $$ Commented by essaad…
Question Number 199084 by universe last updated on 27/Oct/23 $$\:\:\:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\sqrt{\mathrm{n}}} \:\left(\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{n}}\right)^{\mathrm{n}} \mathrm{dx}\:\:\:=\:\:\:\:??? \\ $$ Answered by witcher3 last updated on 27/Oct/23 $$\mathrm{x}=\sqrt{\mathrm{n}}.\mathrm{y}…
Question Number 198952 by ArifinTanjung last updated on 26/Oct/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{tan}\:\mathrm{6x}}\:=\:….? \\ $$ Answered by Mathspace last updated on 26/Oct/23 $${lim}=\frac{\mathrm{3}}{\mathrm{6}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left({sin}\left(\mathrm{3}{x}\right)\sim\mathrm{3}{x}\:{and}\:{tan}\left(\mathrm{6}{x}\right)\sim\mathrm{6}{x}\right) \\ $$…
Question Number 199012 by universe last updated on 26/Oct/23 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{log}\:{n}}{{n}}\:^{\:\:{n}} \sqrt{\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}^{{n}} }{{k}!}}\:\:\:=\:\:\:???? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198839 by Guillaume last updated on 24/Oct/23 $${lim}\:{sin}\left({x}\right)\:=\:? \\ $$$${x}\rightarrow+\infty \\ $$ Commented by Frix last updated on 25/Oct/23 $$\mathrm{Does}\:\mathrm{not}\:\mathrm{exist}. \\ $$ Terms…