Question Number 82519 by peter frank last updated on 22/Feb/20 Commented by mathmax by abdo last updated on 23/Feb/20 $${A}_{\theta} =\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{{n}} }{cos}\left({n}\theta\right)\:\:=\sum_{{n}=\mathrm{0}}…
Question Number 82517 by naka3546 last updated on 22/Feb/20 $$\underset{\:\mathrm{1}} {\int}\overset{\:\infty} {\:}\:\frac{\mathrm{ln}\:{x}}{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:{dx}\:\:,\:\:\:{Convergent}\:\:{or}\:\:{Divergent}\:\:? \\ $$ Commented by Tony Lin last updated on 22/Feb/20 $$\int_{\mathrm{1}} ^{\infty}…
Question Number 16980 by mrW1 last updated on 29/Jun/17 $$\mathrm{To}\:\mathrm{Q16066}: \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{posted}\:\mathrm{my}\:\mathrm{solution}\:\mathrm{there}. \\ $$$$\mathrm{Those}\:\mathrm{who}\:\mathrm{are}\:\mathrm{intetested}\:\mathrm{in}\:\mathrm{this}\:\mathrm{interesting} \\ $$$$\mathrm{question}\:\mathrm{please}\:\mathrm{have}\:\mathrm{a}\:\mathrm{critical}\:\mathrm{view}\:\mathrm{at} \\ $$$$\mathrm{it}.\:\mathrm{Maybe}\:\mathrm{there}\:\mathrm{are}\:\mathrm{alternative}\:\mathrm{solutions} \\ $$$$\mathrm{which}\:\mathrm{are}\:\mathrm{easier}\:\mathrm{and}\:\mathrm{more}\:\mathrm{direct}\:\mathrm{and} \\ $$$$\mathrm{straight}\:\mathrm{on}. \\ $$ Commented…
Question Number 82514 by naka3546 last updated on 22/Feb/20 $${Find}\:\:\:{maximum}\:\:{of}\:\:{n}\:\:{such}\:\:{that}\:\: \\ $$$${n}^{\mathrm{2}} \:+\:{n}\:+\:\mathrm{1}\:\:{is}\:\:{factor}\:\:{of}\:\:\mathrm{19}{n}^{\mathrm{2019}} \:+\:\mathrm{1}\:. \\ $$ Commented by naka3546 last updated on 22/Feb/20 $${n}\:\:\in\:\:\mathbb{N} \\…
Question Number 148048 by puissant last updated on 25/Jul/21 $$\mathrm{2}^{\mathrm{x}} −\mathrm{3}^{\left(\frac{\mathrm{x}}{\mathrm{2}}\right)} =\mathrm{1} \\ $$ Answered by mindispower last updated on 25/Jul/21 $$\mathrm{2}^{{x}} −\left(\sqrt{\mathrm{3}}\right)^{{x}} =\mathrm{1} \\…
Question Number 148051 by abdurehime last updated on 25/Jul/21 $$\rightharpoondown\left(\rightharpoondown\mathrm{p}\rightarrow\mathrm{q}\right)\vee\left(\mathrm{p}\wedge\rightharpoondown\mathrm{q}\right)\: \\ $$$$\mathrm{simplify} \\ $$ Commented by abdurehime last updated on 25/Jul/21 $$\mathrm{please}\:\mathrm{sir}\:\mathrm{help}\:\mathrm{me} \\ $$ Commented…
Question Number 148045 by abdurehime last updated on 25/Jul/21 Commented by abdurehime last updated on 25/Jul/21 $$\mathrm{sorry}?????????????????????????? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 82510 by jagoll last updated on 22/Feb/20 $$\int\:\sqrt{{x}+\sqrt{{x}}\:}\:{dx}\:=\:? \\ $$ Commented by mathmax by abdo last updated on 23/Feb/20 $${I}\:=\int\sqrt{{x}+\sqrt{{x}}}{dx}\:{changement}\:\sqrt{{x}}={t}\:{give}\:{x}={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${I}\:=\int\sqrt{{t}^{\mathrm{2}}…
Question Number 16973 by tawa tawa last updated on 29/Jun/17 $$\mathrm{5}^{\mathrm{log}\left(\mathrm{x}\right)} \:=\:\mathrm{x}^{\mathrm{log}\left(\mathrm{2}\right)} ,\:\:\:\:\:\mathrm{find}\:\:\mathrm{x}. \\ $$ Answered by mrW1 last updated on 29/Jun/17 $$\mathrm{log}\:\left(\mathrm{x}\right)\:\mathrm{log}\:\left(\mathrm{5}\right)=\mathrm{log}\:\left(\mathrm{2}\right)\:\mathrm{log}\:\left(\mathrm{x}\right) \\ $$$$\mathrm{log}\:\left(\mathrm{x}\right)\left[\:\mathrm{log}\:\left(\mathrm{5}\right)−\mathrm{log}\:\left(\mathrm{2}\right)\right]=\mathrm{0}…
Question Number 148043 by mathdanisur last updated on 25/Jul/21 $$\frac{\left(\mathrm{2}\:−\:\sqrt{\mathrm{2}}\right)^{\mathrm{8}} \:\centerdot\:\left(\mathrm{6}\:+\:\mathrm{4}\sqrt{\mathrm{2}}\right)^{\mathrm{8}} }{\left(\mathrm{2}\:+\:\sqrt{\mathrm{2}}\right)^{\mathrm{8}} }\:=\:? \\ $$ Answered by iloveisrael last updated on 25/Jul/21 $$\left[\:\frac{\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)\left(\mathrm{6}+\mathrm{4}\sqrt{\mathrm{2}}\right)}{\mathrm{2}+\sqrt{\mathrm{2}}}\:\right]^{\mathrm{8}} \: \\…