Question Number 200105 by cortano12 last updated on 14/Nov/23 Commented by mr W last updated on 14/Nov/23 Commented by mr W last updated on 14/Nov/23…
Question Number 200103 by cortano12 last updated on 14/Nov/23 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{\mathrm{x}}\:=? \\ $$ Answered by Frix last updated on 14/Nov/23 $$\mathrm{sin}\:\alpha\:−\mathrm{sin}\:\beta\:=\mathrm{2cos}\:\frac{\alpha+\beta}{\mathrm{2}}\:\mathrm{sin}\:\frac{\alpha−\beta}{\mathrm{2}} \\ $$$$\mathrm{For}\:\mathrm{large}\:{x}:\:\frac{\sqrt{{x}+\mathrm{1}}+\sqrt{{x}}}{\mathrm{2}}\sim\sqrt{{x}}\:\wedge\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}}}{\mathrm{2}}\sim\mathrm{0} \\ $$$$\Rightarrow…
Question Number 199983 by cortano12 last updated on 11/Nov/23 $$\:\:\:\mathrm{find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\pi\mathrm{x}}{\mathrm{5}+\mathrm{3x}}\right)\: \\ $$$$\:\:\mathrm{by}\:\mathrm{sequeeze}\:\mathrm{theorem} \\ $$ Answered by tri26112004 last updated on 12/Nov/23 $${We}\:{have}\: \\ $$$$\mid{sin}\left(\:\frac{\pi{x}}{\mathrm{5}+\mathrm{3}{x}}\right)\mid\:\leqslant\:\mathrm{1}…
Question Number 199908 by cortano12 last updated on 11/Nov/23 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{2}^{\mathrm{x}} +\mathrm{3}^{\mathrm{x}} +\mathrm{5}^{\mathrm{x}} }{\mathrm{3}}\right)^{\frac{\mathrm{3}}{\mathrm{x}}} =?\: \\ $$ Answered by cortano12 last updated on 11/Nov/23 $$\:\mathrm{L}\:=\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 199843 by universe last updated on 10/Nov/23 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{1}+{x}\right)\:}−\frac{\mathrm{1}}{\mathrm{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\right)}\right)\:=\:?? \\ $$ Answered by witcher3 last updated on 10/Nov/23 $$=\frac{\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)−\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{ln}\left(\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\right.}= \\…
Question Number 199662 by cortano12 last updated on 07/Nov/23 $$ \\ $$$$\mathrm{A}\:\mathrm{point}\:\mathrm{moves}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{5}}\:\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{it}'\mathrm{s}\:\mathrm{x}−\mathrm{coordinate}\:\mathrm{increases}\: \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{3}\sqrt{\mathrm{10}}\:\:\mathrm{cm}/\mathrm{s}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{it}'\mathrm{s} \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{0}\right) \\ $$$$\mathrm{when}\:\mathrm{x}\:=\:\mathrm{2}…
Question Number 199597 by mnjuly1970 last updated on 05/Nov/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculate}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{Q}\::\:\:\:\:\:\:\mathrm{lim}_{\:{x}\rightarrow\:\frac{\pi}{\mathrm{4}}} \:\:\left(\:\:\mathrm{1}\:+\:\:{sin}\left({x}\right)\:−{cos}\left({x}\right)\:\right)^{\:{tan}\left(\mathrm{2}{x}\right)} \:=\:\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet\:\mathscr{N}{ice}\:−\:\mathscr{M}{athematics}\:\bullet\: \\ $$$$\:\:\:\:\:\:\: \\ $$ 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