Question Number 78392 by jagoll last updated on 17/Jan/20 Answered by john santu last updated on 17/Jan/20 $${let}\:{h}=\:\mathrm{cos}\:{x}\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\sqrt[{\:\:\mathrm{3}}]{\mathrm{cos}\:\mathrm{3}{x}}\:\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{4}{x}}…\:\sqrt[{{n}}]{\mathrm{cos}\:{nx}} \\ $$$${ln}\left({h}\right)=\:{ln}\left(\mathrm{cos}\:{x}\right)+\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{cos}\:\mathrm{2}{x}\right)+\frac{\mathrm{1}}{\mathrm{3}}{ln}\left(\mathrm{cos}\:\mathrm{3}{x}\right)+…+\frac{\mathrm{1}}{{n}}{ln}\left(\mathrm{cos}\:{nx}\right) \\ $$$$\frac{{dh}}{{dx}}=\frac{−\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}−\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{cos}\:\mathrm{2}{x}}−\frac{\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{cos}\:\mathrm{3}{x}}−…−\frac{\mathrm{sin}\:{nx}}{\mathrm{cos}\:{nx}} \\ $$$${now}\:{we}\:{use}\:{L}'{Hopital}\:{rule} \\…
Question Number 78343 by balbayrak last updated on 16/Jan/20 Commented by MJS last updated on 16/Jan/20 $$\mathrm{syntax}\:\mathrm{error}.\:\mathrm{type}\:\mathrm{it}\:\mathrm{correctly}\:\mathrm{please} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 78324 by jagoll last updated on 16/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{4}{x}−\mathrm{cos}\:\mathrm{2}{x}}{\:\sqrt{{x}+\mathrm{1}}−\sqrt{\mathrm{1}−{x}}}= \\ $$ Commented by john santu last updated on 16/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\sqrt{{x}+\mathrm{1}}+\sqrt{\mathrm{1}−{x}}\right)×\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:^{\mathrm{2}} {x}+\mathrm{2sin}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}{x}}…
Question Number 78325 by jagoll last updated on 16/Jan/20 $$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{3}{x}}{\mathrm{5}{x}^{\mathrm{2}} −\mathrm{2}{x}}\right)^{\mathrm{3}{x}−\mathrm{1}} \\ $$ Commented by john santu last updated on 16/Jan/20…
Question Number 12732 by Joel577 last updated on 30/Apr/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}}\:−\:{x}}{\:\sqrt{{x}}\:+\:{x}} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17 $$=\mathrm{1} \\ $$ Commented by…
Question Number 12651 by okhemafrancis last updated on 28/Apr/17 $${find}\:{the}\:{values}\:{of}\:{x}\:{for}\:{which}\:\frac{{x}^{\mathrm{3}} +\mathrm{8}}{{x}^{\mathrm{2}} −\mathrm{4}\:}{is}\:{discontinuous}\:{and}\:{state}\:{each}\:{kinds}\:{of}\:{dicontinuity} \\ $$ Answered by FilupS last updated on 28/Apr/17 $${f}\left({x}\right)=\frac{{x}^{\mathrm{3}} +\mathrm{8}}{{x}^{\mathrm{2}} −\mathrm{4}} \\…
Question Number 143677 by bobhans last updated on 17/Jun/21 Answered by bemath last updated on 17/Jun/21 Answered by mathmax by abdo last updated on 17/Jun/21…
Question Number 78122 by Tony Lin last updated on 14/Jan/20 $$\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}{lnx}\centerdot{ln}\left(\mathrm{1}−{x}\right)=? \\ $$ Commented by msup trace by abdo last updated on 14/Jan/20…
Question Number 78106 by aliesam last updated on 14/Jan/20 Commented by msup trace by abdo last updated on 14/Jan/20 $${let}\:{f}\left({x}\right)={x}^{\mathrm{1}−\xi} \:\int_{{x}} ^{{x}+\mathrm{1}} {sin}\left({t}^{\mathrm{2}} \right){dt} \\…
Question Number 12513 by Joel577 last updated on 24/Apr/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\left[\mathrm{sec}\:\left(\frac{\mathrm{2}}{{x}}\right)\:−\:\mathrm{1}\right] \\ $$ Answered by ajfour last updated on 24/Apr/17 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \left[\frac{\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{2}/{x}\right)}−\mathrm{1}\right] \\…