Question Number 136258 by EDWIN88 last updated on 20/Mar/21 $$\underset{{x}\rightarrow\mathrm{2a}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}−\mathrm{2a}}\:+\:\sqrt{\mathrm{x}}\:−\sqrt{\mathrm{2a}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{4a}^{\mathrm{2}} }}\:=?\:\mathrm{where}\:\mathrm{a}>\mathrm{0} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\:{L}'{H}\ddot {{o}pital}\: \\…
Question Number 5157 by 1771727373 last updated on 24/Apr/16 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+……..={S} \\ $$$$\mathrm{2}+\mathrm{4}+\mathrm{6}+\mathrm{8}+\mathrm{10}+……..=\mathrm{2}{S} \\ $$$${S}\supset\mathrm{2}{S} \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+…………+\left(\mathrm{2}{S}\right)={S} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left\{\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}}\right\}=+\infty \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left\{{n}^{\mathrm{2}} \right\}=+\infty \\ $$$$\left(+\infty\right)+\left(+\infty\right)={S}=\infty…
Question Number 136093 by mnjuly1970 last updated on 18/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:\:\:{calculus}….. \\ $$$$\:\:\:\:\:{calculate}\::: \\ $$$$\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{\:\sqrt{{n}}}\:\underset{{k}=\mathrm{1}\:} {\overset{{n}} {\sum}}{cos}^{\mathrm{2}{n}} \left(\frac{{k}\pi}{{n}}\right)=?? \\ $$$$ \\ $$ Terms of Service…
Question Number 4964 by ankit chakravarti last updated on 27/Mar/16 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right)\centerdot\left(\mathrm{3}+\mathrm{cos}\:{x}\right)}{{x}\centerdot\mathrm{tan4}{x}}=? \\ $$$$ \\ $$ Answered by FilupSmith last updated on 29/Mar/16 Commented by…
Question Number 136026 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{sin}\left(\mathrm{1}−\mathrm{cosx}\right)−\mathrm{xcos}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$ Commented by yutytfjh67ihd last updated on 25/Mar/21 Terms…
Question Number 70364 by 20190927 last updated on 03/Oct/19 $$\mathrm{solve}\:\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} −\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} } \\ $$ Commented by kaivan.ahmadi last updated on 03/Oct/19 $${lim}_{{x}\rightarrow\mathrm{0}} \frac{\left(\mathrm{1}−{x}\right){e}^{{x}} −\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 4712 by paonky last updated on 28/Feb/16 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{1}−\mathrm{sin}{x}} −{e}^{\mathrm{1}−\mathrm{tan}{x}} }{\mathrm{tan}{x}−\mathrm{sin}{x}}=? \\ $$ Answered by Yozzii last updated on 28/Feb/16 $${Let}\:{l}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{1}−{sinx}} −{e}^{\mathrm{1}−{tanx}}…
Question Number 4681 by thachan last updated on 21/Feb/16 $$\int_{\mathrm{4}} ^{\mathrm{cos}\:\underset{\mathrm{4}} {\prod}} \left({x}^{\mathrm{2}} +\mathrm{3}{ax}−\mathrm{5tan}\:\left({x}\right)\right){dx} \\ $$ Commented by prakash jain last updated on 21/Feb/16 $${is}\:{the}\:{upper}\:{limit}\:\mathrm{cos}\:\frac{\pi}{\mathrm{4}}?…
Question Number 4674 by thachan last updated on 20/Feb/16 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}=\mathrm{0} \\ $$ Answered by FilupSmith last updated on 20/Feb/16 $${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$${x}=\frac{−\mathrm{5}\pm\sqrt{\mathrm{25}−\mathrm{4}\left(\mathrm{1}\right)\left(\mathrm{2}\right)}}{\mathrm{2}\left(\mathrm{1}\right)} \\…
Question Number 135742 by mohssinee last updated on 15/Mar/21 Commented by mohssinee last updated on 15/Mar/21 $${help}\:{me}\:! \\ $$ Answered by mathmax by abdo last…