Question Number 142307 by qaz last updated on 29/May/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}\:\left(\mathrm{tan}\:\mathrm{x}\right)−\mathrm{tan}\:\left(\mathrm{tan}\:\left(\mathrm{tan}\:\mathrm{x}\right)\right)}{\mathrm{tan}\:\mathrm{x}\centerdot\mathrm{tan}\:\left(\mathrm{tan}\:\mathrm{x}\right)\centerdot\mathrm{tan}\:\left(\mathrm{tan}\:\left(\mathrm{tan}\:\mathrm{x}\right)\right)}=? \\ $$ Answered by Dwaipayan Shikari last updated on 29/May/21 $${tanx}\approx{x}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\:\:{or}\:\:{x}\:\:\left({sometimes}\right) \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 142300 by qaz last updated on 29/May/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} +\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}} −\left(\mathrm{e}^{\mathrm{tan}\:\mathrm{x}} +\mathrm{tan}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{x}}} }{\mathrm{x}^{\mathrm{3}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 142299 by mnjuly1970 last updated on 29/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 142277 by liberty last updated on 29/May/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−{e}^{\mathrm{sin}\:{x}\:\mathrm{ln}\:\left(\mathrm{cos}\:{x}\right)} }{{x}^{\mathrm{3}} }\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 29/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{e}^{{sinx}\left(−\frac{{x}^{\mathrm{2}}…
Question Number 142204 by mnjuly1970 last updated on 27/May/21 Answered by MJS_new last updated on 28/May/21 $$\mathrm{what}\:\mathrm{are}\:\mathrm{you}\:\mathrm{waiting}\:\mathrm{for}? \\ $$$${A}^{\mathrm{2}} =\begin{bmatrix}{\mathrm{7}}&{\mathrm{2}{m}−\mathrm{5}}&{\mathrm{5}}\\{\mathrm{2}}&{{m}^{\mathrm{2}} −\mathrm{1}}&{{m}+\mathrm{2}}\\{\mathrm{2}}&{\mathrm{2}−{m}}&{\mathrm{9}}\end{bmatrix} \\ $$$${A}^{\mathrm{4}} =\begin{bmatrix}{\mathrm{4}{m}+\mathrm{49}}&{\mathrm{2}{m}^{\mathrm{3}} −\mathrm{5}{m}^{\mathrm{2}}…
Question Number 76630 by Rio Michael last updated on 28/Dec/19 $$\mathrm{two}\:\mathrm{sequences}\:,\:\left({u}_{{n}} \right)\:{and}\:\left({v}_{{n}} \right),\:\mathrm{for}\:{n}\in\mathbb{N}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as}: \\ $$$$\begin{cases}{{u}_{\mathrm{0}} \:=\mathrm{3}}\\{{u}_{{n}+\mathrm{1}} =\:\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}} \:+\:{v}_{{n}} \right)\:\:}\end{cases}\mathrm{and}\:\begin{cases}{{v}_{\mathrm{0}} =\:\mathrm{4}}\\{{v}_{{n}+\mathrm{1}} =\:\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}+\mathrm{1}} \:+\:{v}_{{n}} \right)}\end{cases} \\ $$$$\left.{a}\right)\:\mathrm{calculate}\:{u}_{\mathrm{1}}…
Question Number 142171 by iloveisrael last updated on 27/May/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{\mathrm{sin}\:^{\mathrm{3}} {x}−\mathrm{tan}\:^{\mathrm{3}} {x}}\:=? \\ $$ Answered by iloveisrael last updated on 27/May/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 142151 by iloveisrael last updated on 27/May/21 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\sqrt{{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}}\:=? \\ $$ Commented by gsk2684 last updated on 27/May/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}\:\mathrm{cos}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{x}}}{\mathrm{2}}\mathrm{sin}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}}}{\mathrm{2}}\right) \\ $$$$\mathrm{2}\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{cos}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}}}{\mathrm{2}}\mathrm{sin}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{x}}}\right)…
Question Number 142140 by gsk2684 last updated on 26/May/21 $$\left[\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{{x}}\right]=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100sin}^{−\mathrm{1}} {x}}{{x}}\right]+\left[\frac{\mathrm{100tan}^{−\mathrm{1}} {x}}{{x}}\right]\right\}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100}{x}}{\mathrm{sin}^{−\mathrm{1}} {x}}\right]+\left[\frac{\mathrm{100}{x}}{\mathrm{tan}^{−\mathrm{1}} {x}}\right]\right\}=? \\ $$$${where}\:\left[{x}\right]\:{denotes}\:{greatest}\:{integer}\: \\ $$$${less}\:{than}\:{or}\:{equal}\:{to}\:{x}.…
Question Number 11036 by suci last updated on 08/Mar/17 $${l}\underset{{n}\rightarrow\sim} {{i}m}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{8}{n}^{\mathrm{2}} }{{n}^{\mathrm{4}} +\mathrm{1}}\:=….? \\ $$ Commented by FilupS last updated on 08/Mar/17 $${S}=\underset{{n}\rightarrow\infty}…