Question Number 142150 by iloveisrael last updated on 27/May/21 $$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\right)\:=?\: \\ $$ Commented by liberty last updated on 27/May/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}}…
Question Number 11075 by Joel576 last updated on 10/Mar/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{that}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{75}\:\mathrm{and}\:\mathrm{has}\:\mathrm{exactly}\:\mathrm{75}\:\mathrm{positive} \\ $$$$\mathrm{integral}\:\mathrm{divisors},\:\mathrm{including}\:\mathrm{1}\:\mathrm{and}\:\mathrm{itself}. \\ $$$$\mathrm{Find}\:\frac{{n}}{\mathrm{75}} \\ $$ Commented by FilupS last updated on 11/Mar/17…
Question Number 11074 by Joel576 last updated on 10/Mar/17 $$\frac{\mathrm{2}}{\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}\:} }\:+\:\frac{\mathrm{4}}{\left({y}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{5}}{{z}^{\mathrm{2}} }\:=\:\frac{\mathrm{9}}{\mathrm{4}} \\ $$$$\frac{\mathrm{4}}{\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{2}}{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\mathrm{3}}{\left({z}\:−\:\mathrm{1}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{6}}{\left({y}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{2}}{{z}^{\mathrm{2}} }\:=\:\mathrm{1} \\ $$$$…
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Question Number 142140 by gsk2684 last updated on 26/May/21 $$\left[\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{{x}}\right]=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100sin}^{−\mathrm{1}} {x}}{{x}}\right]+\left[\frac{\mathrm{100tan}^{−\mathrm{1}} {x}}{{x}}\right]\right\}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100}{x}}{\mathrm{sin}^{−\mathrm{1}} {x}}\right]+\left[\frac{\mathrm{100}{x}}{\mathrm{tan}^{−\mathrm{1}} {x}}\right]\right\}=? \\ $$$${where}\:\left[{x}\right]\:{denotes}\:{greatest}\:{integer}\: \\ $$$${less}\:{than}\:{or}\:{equal}\:{to}\:{x}.…
Question Number 11070 by ABD last updated on 10/Mar/17 $${m}\in{Z}\:,\:{x}^{\mathrm{2}} −\left({m}+\mathrm{1}\right){x}+{m}^{\mathrm{2}} −\mathrm{16}=\mathrm{0} \\ $$$${f}\left({x}_{\mathrm{1}} \right)={f}\left({x}_{\mathrm{2}} \right)=\mathrm{0}\:\:,{x}_{\mathrm{1}} <\mathrm{0},\:\mathrm{0}<{x}_{\mathrm{2}} \:\Rightarrow\Sigma{m}=? \\ $$ Answered by mrW1 last updated…
Question Number 11069 by debajeetdey888@gmail.com last updated on 10/Mar/17 Commented by FilupS last updated on 10/Mar/17 $${what} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 11067 by suci last updated on 10/Mar/17 $${if}\:{E}=\left\{{f}\mid{f}:\mathbb{R}\rightarrow\mathbb{R}\:{continuous}\:{function}\:{with}\:{f}\left({x}\right)\in\mathbb{Q},\:\forall{x}\in\mathbb{R}\right\}, \\ $$$${then}\:{E}=….??? \\ $$ Commented by FilupS last updated on 10/Mar/17 $$\mathbb{Q}\:=\:\mathrm{irrational}\:\mathrm{numbers}\:\mathrm{set} \\ $$$$ \\…
Question Number 142138 by mathdanisur last updated on 26/May/21 $$\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}\:+\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:+\:\sqrt{{z}^{\mathrm{2}} +\mathrm{9}}\:=\:\mathrm{10} \\ $$$${x}+{y}+{z}=? \\ $$ Commented by mathdanisur last updated on 27/May/21 $${cool}\:{sir}\:{thank}\:{you}…