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Question Number 132827 Answers: 0 Comments: 2
Question Number 132715 Answers: 4 Comments: 0
$$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{8}^{\mathrm{3}} }+... \\ $$
Question Number 132537 Answers: 1 Comments: 1
$${If}\:{f}\left({x}\right)=\mathrm{8}{x}^{\mathrm{3}\:} +\mathrm{3}{x}\:{then}\:{lim}_{{x}\rightarrow\infty} \frac{{x}^{\mathrm{1}/\mathrm{3}} }{{f}^{−\mathrm{1}} \left(\mathrm{8}{x}\right)−{f}^{−\mathrm{1}} \left({x}\right)}\:{is} \\ $$
Question Number 132434 Answers: 2 Comments: 0
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$
Question Number 132337 Answers: 1 Comments: 0
Question Number 132332 Answers: 0 Comments: 0
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\sqrt{{n}}{e}^{−{n}^{\mathrm{2}} } \\ $$
Question Number 132276 Answers: 0 Comments: 0
Question Number 132274 Answers: 0 Comments: 0
Question Number 132268 Answers: 0 Comments: 0
Question Number 132250 Answers: 0 Comments: 0
Question Number 132173 Answers: 0 Comments: 2
$$\mathrm{If}\:\:\:\:\mathrm{v}\:\:\:=\:\:\:\frac{\sqrt{\mathrm{p}\:\:\:+\:\:\:\frac{\mathrm{1}}{\mathrm{n}}}}{\mathrm{x}},\:\:\:\:\:\:\:\:\:\mathrm{where}\:\:\:\:\mathrm{p}\:\:=\:\:\:\mathrm{pressure}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{dimension}\:\mathrm{of}\:\:\:\:\:\mathrm{n}\:\:\:\mathrm{and}\:\:\:\mathrm{x} \\ $$
Question Number 132162 Answers: 1 Comments: 0
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$
Question Number 132124 Answers: 1 Comments: 2
$$ \\ $$$$\:\:\:\mathrm{Calculate} \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \sqrt{\frac{\mathrm{tan}\left(\mathrm{x}\right)+\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{tan}\left(\mathrm{x}\right)−\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)}}\:\mathrm{cos}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\:\: \\ $$
Question Number 132064 Answers: 0 Comments: 2
Question Number 131935 Answers: 1 Comments: 0
Question Number 131877 Answers: 0 Comments: 4
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left({e}^{\mathrm{2}\pi{n}} −\mathrm{1}\right)} \\ $$
Question Number 131795 Answers: 1 Comments: 0
$$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{10}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{17}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{26}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{37}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{50}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{65}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{82}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{101}^{\mathrm{3}} }+... \\ $$
Question Number 131686 Answers: 1 Comments: 6
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left({n}\pi\right)}{{n}^{\mathrm{3}} } \\ $$
Question Number 131580 Answers: 0 Comments: 2
$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{disprove}} \\ $$$$\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\boldsymbol{{n}}^{\mathrm{2}} +\mathrm{97}\right)^{\mathrm{2}} }=\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{97}\left(\boldsymbol{{e}}^{\boldsymbol{\pi}\sqrt{\mathrm{97}}} −{e}^{−\boldsymbol{\pi}\sqrt{\mathrm{97}}} \right)^{\mathrm{2}} }+\frac{\boldsymbol{\pi}}{\mathrm{388}}.\frac{{e}^{\mathrm{2}\boldsymbol{\pi}\sqrt{\mathrm{97}}} +\mathrm{1}}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi}\sqrt{\mathrm{97}}} −\mathrm{1}}+\frac{\mathrm{37635}}{\mathrm{37636}}−\frac{\mathrm{1}}{\:\mathrm{388}\sqrt{\mathrm{97}}} \\ $$
Question Number 131507 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\mathrm{1}/\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{2019}\right)^{\mathrm{2021}} +\left(\mathrm{2021}\right)^{\mathrm{2019}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{2020} \\ $$$$\:\:\:\mathrm{2}/\mathrm{Show}\:\mathrm{that}\:\mathrm{2222}^{\mathrm{5555}} +\mathrm{5555}^{\mathrm{2222}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{7} \\ $$$$ \\ $$
Question Number 131346 Answers: 0 Comments: 0
Question Number 131094 Answers: 1 Comments: 1
$$\:\: \\ $$$$\:\:\:\mathrm{Calculate} \\ $$$$\:\:\mathrm{1}/\:\mathrm{I}\:=\:\oint_{\mathrm{c}^{+} } \frac{\mathrm{zdz}}{\left(\mathrm{z}−\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{z}^{\mathrm{2}} −\mathrm{2z}+\mathrm{1}−\mathrm{2i}\right)}\:\:,\mathrm{C}=\left\{\mathrm{z}/\mid\mathrm{z}\mid=\mathrm{2}\right\}\: \\ $$$$\:\:\mathrm{2}/\:\mathrm{J}\:=\oint_{\mathrm{c}^{+} } \frac{\mathrm{ch}\left(\mathrm{z}\right)\mathrm{dz}}{\mathrm{z}\left(\mathrm{e}^{\mathrm{z}} −\mathrm{1}\right)}\:\:,\:\:\mathrm{C}=\left\{\mathrm{z}/\mid\mathrm{z}−\mathrm{3i}\mid=\mathrm{4}\right\} \\ $$$$\:\:\mathrm{3}/\:\mathrm{K}=\oint_{\mathrm{c}^{+} } \frac{\mathrm{sin}\left(\mathrm{z}\right)\mathrm{dz}}{\mathrm{z}^{\mathrm{3}} \left(\mathrm{z}+\mathrm{1}\right)^{\mathrm{2}} }\:\:,\:\mathrm{C}=\left\{\mathrm{z}/\mid\mathrm{z}\mid=\mathrm{2}\right\} \\ $$
Question Number 131083 Answers: 0 Comments: 0
$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}−\frac{\mathrm{16}}{\mathrm{13}−\frac{\mathrm{81}}{\mathrm{25}−\frac{\mathrm{256}}{\mathrm{41}−\frac{\mathrm{625}}{\mathrm{61}−\frac{\mathrm{1296}}{\mathrm{85}−\frac{\mathrm{2401}}{\mathrm{113}−...}}}}}}}=\frac{\mathrm{6}}{\boldsymbol{\pi}^{\mathrm{2}} } \\ $$
Question Number 130992 Answers: 1 Comments: 0
$$\mathrm{If}\:\mathrm{I}\:=\:\frac{\mathrm{V}}{\mathrm{R}}\:\mathrm{and}\:\mathrm{V}=\mathrm{250}\:\mathrm{volts}\:\mathrm{and}\:\mathrm{R}=\mathrm{50}\:\mathrm{ohms} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{change}\:\mathrm{in}\:\mathrm{I}\:\mathrm{resulting}\:\mathrm{from}\:\mathrm{an}\: \\ $$$$\mathrm{increase}\:\mathrm{of}\:\mathrm{1}\:\mathrm{volt}\:\mathrm{in}\:\mathrm{V}\:\mathrm{and}\:\mathrm{increase}\:\mathrm{of}\:\mathrm{0}.\mathrm{5}\:\mathrm{ohm} \\ $$$$\mathrm{in}\:\mathrm{R}. \\ $$
Question Number 131078 Answers: 0 Comments: 0
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{8}} +\mathrm{1}} \\ $$
Question Number 130978 Answers: 1 Comments: 5
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