Question Number 2722 by prakash jain last updated on 25/Nov/15 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{series}\:\mathrm{convergent} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{sin}\:{i}}{{i}} \\ $$ Answered by Filup last updated on 25/Nov/15 $$\mathrm{no}…
Question Number 133758 by EDWIN88 last updated on 24/Feb/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}/\mathrm{3}} }\right)\left(\mathrm{tan}^{−\mathrm{1}} \sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}\:−\mathrm{tan}^{−\mathrm{1}} \sqrt[{\mathrm{3}}]{{x}−\mathrm{1}}\:\right)=? \\ $$ Answered by liberty last updated on 24/Feb/21 $$\left(\mathrm{i}\right)\:\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}/\mathrm{3}}…
Question Number 68178 by Mikael last updated on 06/Sep/19 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\left({cosx}\right)^{{sin}\mathrm{2}{x}} −\mathrm{1}}{{x}^{\mathrm{3}} }=? \\ $$ Commented by mathmax by abdo last updated on 06/Sep/19 $${let}\:{f}\left({x}\right)\:=\frac{\left({cosx}\right)^{{sin}\left(\mathrm{2}{x}\right)}…
Question Number 2624 by prakash jain last updated on 23/Nov/15 $$\mathrm{Old}\:\mathrm{question}\:\mathrm{related}\:\mathrm{to}\:\mathrm{greatest}\:\mathrm{int}\:\mathrm{function}. \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\lfloor\mathrm{1}+{x}\rfloor=\mathrm{1} \\ $$$$\lfloor\mathrm{1}\rfloor=\mathrm{1} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\lfloor\mathrm{1}−{x}\rfloor=? \\ $$ Answered by Filup last…
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Question Number 133583 by bemath last updated on 23/Feb/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{24}}}{\mathrm{x}^{\mathrm{6}} } \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 67996 by TawaTawa last updated on 03/Sep/19 Commented by mathmax by abdo last updated on 03/Sep/19 $${we}\:{have}\:\:\mathrm{1}\leqslant{k}\leqslant{n}\:\Rightarrow{n}^{\mathrm{2}} +\mathrm{1}\leqslant{n}^{\mathrm{2}} \:+{k}\leqslant{n}^{\mathrm{2}} \:+{n}\:\Rightarrow \\ $$$$\sqrt{{n}^{\mathrm{2}} \:+\mathrm{1}}\leqslant\sqrt{{n}^{\mathrm{2}}…
Question Number 133494 by Eric002 last updated on 22/Feb/21 $${solve}\:{without}\:{using}\:{l}'{hopital}\:{and}\:{series}\: \\ $$$$\underset{{x}\rightarrow\mathrm{8}} {\mathrm{lim}}\frac{{x}\:\sqrt[{\mathrm{3}}]{{x}}−\mathrm{16}}{{x}−\mathrm{8}} \\ $$ Answered by Olaf last updated on 22/Feb/21 $$ \\ $$$$\mathrm{X}\:=\:\frac{{x}\sqrt[{\mathrm{3}}]{{x}}−\mathrm{16}}{{x}−\mathrm{8}}…
Question Number 133462 by benjo_mathlover last updated on 22/Feb/21 Answered by TheSupreme last updated on 22/Feb/21 $${both}\:{converge} \\ $$ Commented by benjo_mathlover last updated on…
Question Number 133454 by rs4089 last updated on 22/Feb/21 Answered by TheSupreme last updated on 22/Feb/21 $$\Omega=\left\{\left({x},{y}\right)\mid\:{x}>\mathrm{0}\:;\:\mathrm{0}<{y}<{x}\right\} \\ $$$$\Omega=\left\{\left({x},{y}\right)\mid\:{y}>\mathrm{0},\:{x}>{y}\right\} \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{{x}} {e}^{−{xy}}…