Question Number 13252 by raktim Ghosh last updated on 17/May/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}sin}\:\mathrm{x} \\ $$ Answered by Abbas-Nahi last updated on 17/May/17 $$={x}\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\frac{\mathrm{sin}\:{x}}{{x}} \\ $$$$=\mathrm{0}\:\left(\mathrm{1}\right)\:\:;{since}\left({li}\underset{×\rightarrow\mathrm{0}}…
Question Number 78693 by TawaTawa last updated on 19/Jan/20 Commented by abdomathmax last updated on 20/Jan/20 $${let}\:{f}\left({x}\right)=\frac{\left(^{\mathrm{3}} \sqrt{{x}}\right)+\left(^{\mathrm{3}} \sqrt{{a}}\right)}{{x}+{a}}\:\:{changement}\:{x}+{a}={t}\:{give} \\ $$$${f}\left({x}\right)={g}\left({t}\right)=\frac{\left(^{\mathrm{3}} \sqrt{{t}−{a}}+\left(^{\mathrm{3}} \sqrt{{a}}\right)\right.}{{t}}\:{we}\:{hsve} \\ $$$$\alpha^{\mathrm{3}}…
Question Number 78682 by Omer Alattas last updated on 19/Jan/20 Commented by mathmax by abdo last updated on 19/Jan/20 $${we}\:{have}\:\left({sinx}\right)^{{x}} ={e}^{{xln}\left({sinx}\right)} \:\:{and}\:{xln}\left({sinx}\right)\sim{xlnx}\:\:\left({x}\rightarrow\mathrm{0}\right)\Rightarrow \\ $$$${lim}_{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 144204 by bemath last updated on 23/Jun/21 $$\mathrm{Find}\:\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{f}\left(\mathrm{2h}+\mathrm{2}+\mathrm{h}^{\mathrm{2}} \right)−\mathrm{f}\left(\mathrm{2}\right)}{\mathrm{f}\left(\mathrm{h}−\mathrm{h}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{f}\left(\mathrm{1}\right)}=? \\ $$$$\mathrm{if}\:\mathrm{given}\:\mathrm{that}\:\begin{cases}{\mathrm{f}\:'\left(\mathrm{2}\right)=\mathrm{6}}\\{\mathrm{f}\:'\left(\mathrm{1}\right)=\mathrm{4}}\end{cases} \\ $$ Answered by bramlexs22 last updated on 23/Jun/21 $$\:\underset{\mathrm{h}\rightarrow\mathrm{0}}…
Question Number 78635 by Pratah last updated on 19/Jan/20 Commented by john santu last updated on 19/Jan/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\underset{{n}} {\overset{\mathrm{2}{n}} {\int}}\:\left(\frac{{x}}{{x}^{\mathrm{5}} +\mathrm{1}}\right){dx}\:}{{n}^{−\mathrm{3}} }\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\frac{\mathrm{2}{n}}{\mathrm{32}{n}^{\mathrm{5}} +\mathrm{1}}\right).\mathrm{2}−\left(\frac{{n}}{{n}^{\mathrm{5}}…
Question Number 78596 by jagoll last updated on 19/Jan/20 $$ \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{1}−\mathrm{3tan}\:^{\mathrm{2}} \mathrm{x}\right)^{\frac{\mathrm{2}}{\mathrm{sin}\:^{\mathrm{2}} \:\mathrm{3x}}\:\:\:} =\:?\: \\ $$ Commented by mathmax by abdo…
Question Number 413 by 123456 last updated on 25/Jan/15 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\:\frac{\left({x}+{y}\right)\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }} \\ $$ Answered by prakash jain last updated on 31/Dec/14…
Question Number 412 by 123456 last updated on 25/Jan/15 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\frac{\mathrm{sin}\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }} \\ $$ Answered by prakash jain last updated on 31/Dec/14…
Question Number 394 by prakash jain last updated on 27/Dec/14 $${f}\left({x}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{i}} {x}^{{i}} \\ $$$${a}_{{i}} \:\:\mathrm{A}\:\mathrm{constant}\:\mathrm{independent}\:\mathrm{of}\:{x} \\ $$$$\mathrm{I}{s}\:\mathrm{the}\:\mathrm{below}\:\mathrm{statement}\:\mathrm{correct}? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{0} \\ $$$$\mathrm{If}\:\mathrm{not}\:\mathrm{give}\:\mathrm{an}\:\mathrm{example}. \\…
Question Number 379 by userid1 last updated on 25/Jan/15 $$\mathrm{Find}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{e}^{\mathrm{1}/{x}} −\mathrm{1}}{{e}^{\mathrm{1}/{x}} +\mathrm{1}}\right) \\ $$ Commented by 123456 last updated on 25/Dec/14 $$\underset{{x}\rightarrow\mathrm{0}+} {\mathrm{lim}}\frac{{e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{{e}^{\frac{\mathrm{1}}{{x}}}…