Question Number 32279 by abdo imad last updated on 22/Mar/18 $${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{tan}^{\mathrm{2}} {x}}{\left(\mathrm{1}−{cosx}\right)}\:.\frac{{e}^{{x}} \:−\mathrm{1}}{{x}}\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32278 by abdo imad last updated on 22/Mar/18 $${calculate}\:{lim}_{{x}\rightarrow+\infty} \left({x}−\mathrm{1}\right){cos}\left(\frac{\pi}{{x}}\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97807 by Ar Brandon last updated on 09/Jun/20 $$\mathcal{G}\mathrm{iven}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} ,\:\mathrm{suppose}\:\left(\mathrm{u}_{\mathrm{2n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{and}\:\left(\mathrm{u}_{\mathrm{2n}+\mathrm{1}} \right)_{\mathrm{n}\in\mathbb{N}} \\ $$$$\mathrm{converge}\:\mathrm{towards}\:\mathrm{the}\:\mathrm{same}\:\mathrm{limit},\:\mathrm{L}. \\ $$$$\mathcal{S}\mathrm{how}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{equally}\:\mathrm{converges}\:\mathrm{to}\:\mathrm{L}. \\ $$ Terms…
Question Number 32255 by abdo imad last updated on 22/Mar/18 $${le}\:{x}>\mathrm{0}\:{and}\:{a}>\mathrm{0}\:{find}\:{lim}_{{x}\rightarrow{a}} \:\frac{{log}_{{a}} \:\left({x}\right)\:−{log}_{{x}} \left({a}\right)}{{sinx}\:−{sina}}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32256 by abdo imad last updated on 22/Mar/18 $$\left.\mathrm{1}\right){let}\:{a}>\mathrm{0}\:{and}\:{x}>\mathrm{0}\:{find}\:{lim}\:_{{x}\rightarrow{a}} \:\frac{{e}^{−{ax}^{\mathrm{2}} } \:−\:{e}^{−{xa}^{\mathrm{2}} } }{{a}^{{x}} \:−{x}^{{a}} }\:. \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{x}\rightarrow\mathrm{2}} \:\:\:\frac{{e}^{−\mathrm{2}{x}^{\mathrm{2}} } \:−\:{e}^{−\mathrm{4}{x}} }{\mathrm{2}^{{x}} \:−{x}^{\mathrm{2}}…
Question Number 97781 by Ar Brandon last updated on 09/Jun/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{sequences}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{and}\:\left(\mathrm{v}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \mathrm{defined} \\ $$$$\mathrm{by}\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}!}\:\mathrm{and}\:\mathrm{v}_{\mathrm{n}} =\mathrm{u}_{\mathrm{n}} +\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}!\right)} \\ $$$$\mathrm{a}\backslash\:\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}}…
Question Number 163214 by cortano1 last updated on 05/Jan/22 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:{x}−\mathrm{2tan}\:{x}+{x}^{\mathrm{3}} }{\mathrm{6}{x}−\mathrm{2sin}\:\mathrm{3}{x}−\mathrm{9}{x}^{\mathrm{3}} }\:=? \\ $$ Commented by blackmamba last updated on 05/Jan/22 $$\:\mathcal{L}\:=\:\frac{\mathrm{5}}{\mathrm{81}} \\ $$…
Question Number 32137 by Joel578 last updated on 20/Mar/18 $$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\:\frac{{f}\left({x}\right){g}\left({x}\right)\:−\:\mathrm{3}{g}\left({x}\right)\:−\:\mathrm{3}}{{f}\left({x}\right)\:−\:\mathrm{3}\left({x}\:−\:\mathrm{5}\right)}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{g}'\left(\mathrm{5}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97577 by Rio Michael last updated on 08/Jun/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{4}{x}\:\mathrm{ln}{x}}{{x}−\mathrm{1}}\:=?? \\ $$ Commented by Dwaipayan Shikari last updated on 23/Jun/20 $$\mathrm{4}\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{xlog}\left(\mathrm{1}+{x}−\mathrm{1}\right)}{{x}−\mathrm{1}}=\mathrm{4} \\…
Question Number 32008 by gunawan last updated on 18/Mar/18 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left[\left(\frac{\mathrm{1}}{{n}}\right)^{{n}} +\left(\frac{\mathrm{2}}{{n}}\right)^{{n}} +..+\left(\frac{{n}}{{n}}\right)^{{n}} \right]=… \\ $$ Commented by JDamian last updated on 18/Mar/18 $${I}\:{guess}\:{the}\:{use}\:{of}\:\boldsymbol{{x}}\:{is}\:{a}\:{typo}. \\…