Question Number 31511 by abdo imad last updated on 09/Mar/18 $${f}\:{is}\:{C}^{\mathrm{2}} \:{inside}\:{R}\:{and}\:{a}\in{R}\:{find} \\ $$$${lim}_{{h}\rightarrow\mathrm{0}} \:\frac{\left.{fa}+{h}\right)−\mathrm{2}{f}\left({a}\right)\:+{f}\left({a}−{h}\right)}{{h}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31461 by abdo imad last updated on 08/Mar/18 $${let}\:{give}\:\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}\:\left(\frac{{k}}{{n}}\right)\:{sin}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:{is}\:{convergent} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{u}_{{n}} . \\ $$ Terms…
Question Number 162523 by cortano last updated on 30/Dec/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{7tan}\:{x}−\mathrm{tan}\:\mathrm{7}{x}}{{x}^{\mathrm{3}} }\:=? \\ $$ Answered by Ar Brandon last updated on 30/Dec/21 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{7tan}{x}−\mathrm{tan7}{x}}{{x}^{\mathrm{3}} }…
Question Number 96977 by 175 last updated on 05/Jun/20 $$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\:\frac{{x}\:−\:\mathrm{5}}{\mathrm{2}\:+\:\mathrm{cot}^{\mathrm{2}} \frac{\mathrm{2}}{{x}\:−\mathrm{5}}} \\ $$ Answered by mathmax by abdo last updated on 06/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{x}−\mathrm{5}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{tan}^{\mathrm{2}} \left(\frac{\mathrm{2}}{\mathrm{x}−\mathrm{5}}\right)}}\:\:\mathrm{changement}\:\mathrm{x}−\mathrm{5}\:=\mathrm{t}\:\mathrm{give}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{t}\right)…
Question Number 162510 by cortano last updated on 30/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{7tan}\:{x}−\mathrm{tan}\:\mathrm{7}{x}}{\mathrm{3}{x}}\:=? \\ $$ Answered by Lordose last updated on 30/Dec/21 $$\mathrm{L}−\mathrm{Hopital}'\mathrm{s};\:\frac{\mathrm{7sec}^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{7sec}^{\mathrm{2}} \left(\mathrm{7x}\right)}{\mathrm{3}}\:=\:\frac{\mathrm{0}}{\mathrm{3}}\:=\:\mathrm{0} \\ $$…
Question Number 96931 by bobhans last updated on 05/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{5x}^{\mathrm{4}} −\mathrm{8}}{\mathrm{7x}^{\mathrm{3}} +\mathrm{2}}×\mathrm{tan}\:\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\:=? \\ $$ Commented by PRITHWISH SEN 2 last updated on 05/Jun/20 $$\underset{{x}\rightarrow\infty}…
Question Number 162398 by qaz last updated on 29/Dec/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{arctan}\:\left(\mathrm{t}+\mathrm{sin}\:\mathrm{x}\right)−\mathrm{arctan}\:\mathrm{t}\right)\mathrm{dt}}{\mathrm{arctan}\:\mathrm{x}}=? \\ $$ Answered by aleks041103 last updated on 29/Dec/21 $${both}\:{go}\:{to}\:\mathrm{0} \\ $$$${use}\:{l}'{hopital}…
Question Number 162399 by cortano last updated on 29/Dec/21 $$\:\:{Let}\:{m}\:\&\:{n}\:{be}\:{two}\:{positive}\:{numbers}\: \\ $$$$\:{greater}\:{than}\:\mathrm{1}\:.\:{If}\:\underset{{p}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{\mathrm{cos}\:\left({p}^{{n}} \right)} −{e}}{{p}^{{m}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}}{e}\: \\ $$$$\:{then}\:\frac{{n}}{{m}}=? \\ $$ Commented by blackmamba last updated…
Question Number 162364 by cortano last updated on 29/Dec/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5sin}\:{x}−\mathrm{sin}\:\mathrm{3}{x}\:\mathrm{cos}\:\mathrm{2}{x}−\mathrm{cos}\:\mathrm{3}{x}\:\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{3}} }\:=? \\ $$ Commented by blackmamba last updated on 29/Dec/21 $$\:{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5sin}\:{x}−\mathrm{sin}\:\mathrm{5}{x}}{{x}^{\mathrm{3}} } \\…
Question Number 31246 by malwaan last updated on 04/Mar/18 $$\mathrm{without}\:\mathrm{using}\:\mathrm{lohpital} \\ $$$$\mathrm{find} \\ $$$$\underset{\mathrm{x}\rightarrow\pi/\mathrm{6}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{2sinx}}{\mathrm{cos}\:\mathrm{3x}} \\ $$ Commented by malwaan last updated on 04/Mar/18 $$\mathrm{please}…