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}\:! \\ $$ Answered by mathmax by abdo last…
Question Number 4589 by FilupSmith last updated on 09/Feb/16 $${a}_{{n}} =\sqrt{\mathrm{2}+{a}_{{n}−\mathrm{1}} } \\ $$$${a}_{\mathrm{1}} =\sqrt{\mathrm{2}} \\ $$$$ \\ $$$${L}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} =\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+…}}}} \\ $$$${L}=? \\ $$…
Question Number 4587 by FilupSmith last updated on 09/Feb/16 $${L}=\underset{{i}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} {i}}{{i}+\mathrm{1}} \\ $$$${L}=? \\ $$ Commented by Yozzii last updated on 14/Feb/16 $${L}\:{does}\:{not}\:{exist}.\:{While}\:\mid{L}\mid=\underset{{i}\rightarrow\infty} {\mathrm{lim}}\frac{{i}}{{i}+\mathrm{1}}…
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Question Number 4500 by FilupSmith last updated on 02/Feb/16 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{n}!}{{n}^{{n}} }={L} \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{for}\:{L} \\ $$ Commented by Yozzii last updated on 02/Feb/16…
Question Number 135571 by bemath last updated on 14/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}}{\left({k}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{8}}\:=? \\ $$ Commented by EDWIN88 last updated on 14/Mar/21 $$\mathrm{i}\:\mathrm{guess}\:\mathrm{the}\:\mathrm{series}\:\mathrm{should}\:\mathrm{be}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{k}}{\left(\mathrm{k}^{\mathrm{2}}…