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\} \\ $$$$\Omega=\left\{\left({x},{y}\right)\mid\:{y}>\mathrm{0},\:{x}>{y}\right\} \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{{x}} {e}^{−{xy}}…
Question Number 2322 by prakash jain last updated on 15/Nov/15 $${a}_{\mathrm{0}} ={x} \\ $$$${a}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{1}+{a}_{{n}} } \\ $$$$\mathrm{Find}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{for}\:{x}\:\mathrm{such}\:\mathrm{that} \\ $$$${a}_{{n}} =−\mathrm{1}\:\mathrm{for}\:\mathrm{some}\:{n}\in\mathbb{N}. \\ $$$$\mathrm{For}\:\mathrm{example}:\: \\ $$$${x}=−\mathrm{2},\:{a}_{\mathrm{1}}…
Question Number 2297 by prakash jain last updated on 14/Nov/15 $${a}_{\mathrm{0}} ={k} \\ $$$${a}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{1}+{a}_{{n}} } \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{a}_{{n}} =? \\ $$ Commented by Yozzi…
Question Number 2265 by B744237509 last updated on 12/Nov/15 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3}{x}+{sin}\mathrm{2}{x}}{\mathrm{2}{x}+{sin}\mathrm{3}{x}}=? \\ $$$$ \\ $$$$ \\ $$ Answered by Filup last updated on 12/Nov/15 $$=\underset{{x}\rightarrow\mathrm{0}}…