Question Number 3048 by Syaka last updated on 03/Dec/15 $$\left.\mathrm{1}\right)\:\underset{{x}\:\rightarrow\:−\infty} {{lim}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\right)_{} ^{{x}\:} \:=\:? \\ $$$$ \\ $$$$ \\ $$ Answered by 123456 last updated on…
Question Number 134117 by ClarkeMelodyWenkeh last updated on 27/Feb/21 Answered by TheSupreme last updated on 28/Feb/21 $${A}=\mathrm{15} \\ $$$${B}=\mathrm{10} \\ $$$${A}\cup{B}={A}+{B}−{A}\cap{B}=\mathrm{20} \\ $$$${A}\cap{B}=\mathrm{15}+\mathrm{10}−\mathrm{20}=\mathrm{5} \\ $$$${p}\left({A}\cap{B}\right)=\frac{{A}\cap{B}}{{A}\cup{B}}=\frac{\mathrm{1}}{\mathrm{4}}…
Question Number 134116 by ClarkeMelodyWenkeh last updated on 27/Feb/21 Answered by EDWIN88 last updated on 27/Feb/21 $$\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}+\mathrm{3}\right)−\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{8}\right) \\ $$$$\:\Leftrightarrow\:\frac{\mathrm{x}+\mathrm{3}}{\mathrm{x}}\:=\:\mathrm{8}\:,\:\mathrm{3}\:=\:\mathrm{7x}\:,\:\mathrm{x}\:=\:\frac{\mathrm{3}}{\mathrm{7}} \\ $$ Terms…
Question Number 3046 by Filup last updated on 03/Dec/15 $$\int_{\mathrm{0}} ^{\:{n}} {x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}+{n}\right){dx}=? \\ $$$$\left({x},\:{n}\right)\in\mathbb{R} \\ $$ Commented by Filup last updated on 04/Dec/15 $${x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}+{n}\right)=\frac{\left({x}+{n}\right)!}{\left({x}−\mathrm{1}\right)!} \\…
Question Number 134118 by ClarkeMelodyWenkeh last updated on 27/Feb/21 Answered by EDWIN88 last updated on 27/Feb/21 $$\left(\mathrm{i}\right)\:\angle\mathrm{POS}\:=\:\mathrm{2}×\angle\:\mathrm{PTS}\:=\:\mathrm{116}° \\ $$$$\left(\mathrm{ii}\right)\:\angle\:\mathrm{PRS}\:=\:\mathrm{180}°−\angle\mathrm{PTS}\:=\:\mathrm{122}°\: \\ $$ Commented by otchereabdullai@gmail.com last…
Question Number 3044 by 123456 last updated on 03/Dec/15 $$\mathrm{random}\:\mathrm{question} \\ $$$$\mathrm{if}\:\mathrm{person}\:\mathrm{as}\:\mathrm{5}\:\mathrm{years}\:\mathrm{old}\:\mathrm{and}\:\left(\mathrm{s}\right)\mathrm{he}\:\mathrm{back} \\ $$$$\mathrm{10}\:\mathrm{years}\:\mathrm{in}\:\mathrm{time}\:\left(\mathrm{by}\:\mathrm{some}\:\mathrm{mean}\right) \\ $$$$\mathrm{would}\:\left(\mathrm{s}\right)\mathrm{he}\:\mathrm{have}\:−\mathrm{5}\:\mathrm{years}\:\mathrm{old}? \\ $$ Answered by Filup last updated on 03/Dec/15…
Question Number 68576 by naka3546 last updated on 13/Sep/19 Commented by naka3546 last updated on 13/Sep/19 $${Find}\:\:{a}\:\:,\:\:{if}\:\:\left[\:{yellow}\:\right]\:=\:\:\left[\:{blue}\:\right] \\ $$$${Area}\:\:{of}\:\:{yellow}\:\:=\:\:{area}\:\:{of}\:\:{blue} \\ $$ Answered by mr W…
Question Number 134108 by Eric002 last updated on 27/Feb/21 $$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{4}}]{\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}}\right) \\ $$ Answered by Ñï= last updated on 27/Feb/21 $$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{4}}]{\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}}\right) \\…
Question Number 134110 by mohammad17 last updated on 27/Feb/21 Answered by mr W last updated on 27/Feb/21 $$\mathrm{log}\:\left({LHS}\right) \\ $$$$=\mathrm{log}\:\frac{{y}}{{z}}×\mathrm{log}\:{x}+\mathrm{log}\:\frac{{z}}{{x}}×\mathrm{log}\:{y}+\mathrm{log}\:\frac{{x}}{{y}}×\mathrm{log}\:{z} \\ $$$$=\left(\mathrm{log}\:{y}−\mathrm{log}\:{z}\right)\mathrm{log}\:{x}+\left(\mathrm{log}\:{z}−\mathrm{log}\:{x}\right)\mathrm{log}\:{y}+\left(\mathrm{log}\:{x}−\mathrm{log}\:{y}\right)\mathrm{log}\:{z} \\ $$$$=\mathrm{log}\:{y}\:\mathrm{log}\:{x}−\mathrm{log}\:{z}\:\mathrm{log}\:{x}+\mathrm{log}\:{z}\:\mathrm{log}\:{y}−\mathrm{log}\:{x}\:\mathrm{log}\:{y}+\mathrm{log}\:{x}\:\mathrm{log}\:{z}−\mathrm{log}\:{y}\:\mathrm{log}\:{z} \\…
Question Number 3035 by 123456 last updated on 03/Dec/15 $$\omega\left({z}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}^{{z}} \left[{z}+\left({z}+\mathrm{1}\right)+…+\left({z}+{n}\right)\right]}{{z}\left({z}+\mathrm{1}\right)\left({z}+\mathrm{2}\right)…\left({z}+{n}\right)} \\ $$$$\omega\left(\mathrm{1}\right)=? \\ $$ Commented by prakash jain last updated on 04/Dec/15 $${w}\left(\mathrm{1}\right)=\underset{{n}\rightarrow\infty}…