Question Number 44795 by behi83417@gmail.com last updated on 04/Oct/18 Commented by maxmathsup by imad last updated on 05/Oct/18 $${let}\:{A}\left({x}\right)=\left(\frac{{sinx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \:\Rightarrow{ln}\left({A}_{} \left({x}\right)\right)=\frac{\mathrm{1}}{{x}^{\mathrm{2}} }{ln}\left(\frac{{sinx}}{{x}}\right)\:{but} \\ $$$${sinx}\:={x}−\frac{{x}^{\mathrm{3}}…
Question Number 110307 by bemath last updated on 28/Aug/20 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{3}−\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{arctan}\:\left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{x}−{x}^{\mathrm{2}} }\right)\:{dx} \\ $$$$\left(\mathrm{3}\right){how}\:{many}\:{integer}\:{solution}\:{sets} \\ $$$${exist}\:{for}\:{the}\:{equation}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2} \\ $$…
Question Number 110260 by bemath last updated on 28/Aug/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\:\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}}\right)\:? \\ $$ Answered by john santu last updated on 28/Aug/20 $${we}\:{know}\:{that}\:−\mathrm{1}\leqslant\mathrm{cos}\:\frac{\mathrm{1}}{{x}}\leqslant\mathrm{1}\: \\ $$$${so}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}{x}\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}}\right)=\:\infty…
Question Number 175765 by sciencestudent last updated on 06/Sep/22 $${li}\underset{{x}\rightarrow\infty} {{m}}\left(\mathrm{1}+\frac{\mathrm{2}}{{x}}\right)^{−{x}} =? \\ $$ Answered by Ar Brandon last updated on 06/Sep/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{2}}{{x}}\right)^{−{x}} \\…
Question Number 175762 by infinityaction last updated on 06/Sep/22 $$\:\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{\mathrm{lim}}}\left(\left[\frac{\boldsymbol{\mathrm{nsinx}}\:}{\boldsymbol{\mathrm{x}}}\right]+\left[\frac{\boldsymbol{\mathrm{ntanx}}\:}{\boldsymbol{\mathrm{x}}}\right]\right)\:,\:\boldsymbol{\mathrm{where}}\:\left[:\right]\:\boldsymbol{\mathrm{denotes}} \\ $$$$\:\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{greatest}}\:\boldsymbol{\mathrm{integer}}\:\boldsymbol{\mathrm{function}}\:\:\boldsymbol{\mathrm{and}}\: \\ $$$$\:\:\boldsymbol{\mathrm{n}}\in\mathbb{I}−\left\{\mathrm{0}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44652 by rahul 19 last updated on 02/Oct/18 $${Prove}\:{that}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{ax}\right)^{\frac{\mathrm{1}}{{b}}} −\mathrm{1}}{{x}}\:=\:\frac{{a}}{{b}}. \\ $$ Commented by rahul 19 last updated on 02/Oct/18 $${without}\:{using}\:{L}−{hospital}\:{rule}. \\…
Question Number 110132 by bemath last updated on 27/Aug/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{5cos}\:^{\mathrm{2}} {x}−\mathrm{2cos}\:{x}−\mathrm{3}}{\mathrm{cos}\:{x}−\mathrm{cos}\:\mathrm{3}{x}}\:? \\ $$ Commented by PRITHWISH SEN 2 last updated on 27/Aug/20 $$\mathrm{form}\:\frac{\mathrm{0}}{\mathrm{0}}\:\mathrm{use}\:\mathrm{L}'\mathrm{Hopital} \\…
Question Number 110095 by bemath last updated on 27/Aug/20 $$\:\:\:\left[\frac{{be}}{{math}}\right] \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}}\right) \\ $$ Answered by john santu last updated on 27/Aug/20 $$\:\:\:\:{let}\:\frac{\mathrm{1}}{{x}}\:=\:{h}\:\begin{cases}{{x}\rightarrow\mathrm{0}}\\{{h}\rightarrow\infty}\end{cases}…
Question Number 110086 by john santu last updated on 27/Aug/20 $$\:\:\frac{\spadesuit{JS}\spadesuit}{\bigstar\blacksquare.\bigstar} \\ $$$${If}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +\mathrm{2}\mid{ax}\mid−\mathrm{3}{a}^{\mathrm{2}} }{\:\sqrt{{x}}−\sqrt{{a}}\:}\:=\:{P}\:,\:{with}\:{a}>\mathrm{0} \\ $$$${then}\:{the}\:{value}\:{of}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\mathrm{2}{x}^{\mathrm{2}} −\mid{ax}\mid−{a}^{\mathrm{2}} }{{x}−{a}}\:{is} \\ $$$$\_\_\_ \\ $$$$\:\left({a}\right)\:\frac{\mathrm{3}{P}}{\mathrm{4}\sqrt{{a}}}\:\:\:\:\:\:\left({b}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}\sqrt{{a}}}\:\:\:\:\:\left({c}\right)\:\frac{\mathrm{8}{P}}{\mathrm{3}\sqrt{{a}}}…
Question Number 110075 by bemath last updated on 27/Aug/20 $$\:\:\bigtriangleup\frac{{be}}{{math}}\bigtriangledown \\ $$$$\:\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}.\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} .\mathrm{sin}\:{x}}\:? \\ $$$$\left(\mathrm{2}\right)\:{find}\:\frac{{dy}}{{dx}}\:{from}\:\frac{{x}+{y}}{{x}−{y}}\:=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$ Commented by bobhans last updated on…