Question Number 84576 by msup trace by abdo last updated on 14/Mar/20 $${find}\:{locus}\:{of}\:\:\:\mid{z}−\frac{\mathrm{1}}{{z}}\mid=\mathrm{2}\mid\overset{−} {{z}}\mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84579 by msup trace by abdo last updated on 14/Mar/20 $${find}\:\int\:\left({x}^{\mathrm{2}} −\mathrm{2}\right)\sqrt{{x}+\frac{\mathrm{1}}{{x}}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84575 by msup trace by abdo last updated on 14/Mar/20 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\Gamma\left(\frac{\mathrm{1}}{{n}}\right) \\ $$$$\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:\:\:\:\left({x}>\mathrm{0}\right) \\ $$ Terms of…
Question Number 84572 by msup trace by abdo last updated on 14/Mar/20 $${let}\:\:{F}\left({z}\right)\:=\frac{{z}^{\mathrm{2}} }{\mathrm{1}+{z}^{\mathrm{7}} } \\ $$$$\left.\mathrm{1}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${z}^{\mathrm{7}} \:+\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right) \\ $$$${the}\:{fraction}\:{F}\left({x}\right) \\…
Question Number 84571 by msup trace by abdo last updated on 14/Mar/20 $${calculate}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\:\sqrt{{k}}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150044 by bramlexs22 last updated on 09/Aug/21 $$\:\mathrm{Given}\:\mathrm{f}\left(\frac{\mathrm{2x}−\mathrm{3}}{\mathrm{2x}+\mathrm{1}}\right)+\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{1}−\mathrm{2x}}\right)=\:\mathrm{4x} \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Answered by liberty last updated on 09/Aug/21 $$\:\mathrm{f}\left(\frac{\mathrm{2x}−\mathrm{3}}{\mathrm{2x}+\mathrm{1}}\right)+\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{1}−\mathrm{2x}}\right)=\mathrm{4x}\:\ldots\left(\mathrm{i}\right) \\ $$$$\mathrm{let}\:\frac{\mathrm{2x}−\mathrm{3}}{\mathrm{2x}+\mathrm{1}}\:=\:\mathrm{y}\:; \\…
Question Number 84448 by jagoll last updated on 13/Mar/20 $$\mathrm{5}^{\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{7}\mid\mathrm{x}\mid+\mathrm{10}}{\mathrm{x}^{\mathrm{2}} −\mathrm{6x}+\mathrm{9}}} \:<\:\mathrm{1} \\ $$ Answered by john santu last updated on 13/Mar/20 $$\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{7}\mid\mathrm{x}\mid+\mathrm{10}}{\mathrm{x}^{\mathrm{2}}…
Question Number 18859 by myintkhaing last updated on 31/Jul/17 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}+\mathrm{2}\right)=\mathrm{f}\left(\mathrm{x}\right)+\mathrm{7}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{2};\:\mathrm{f}\left(\mathrm{2}\right)=\mathrm{5}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{150}\right)\:\mathrm{to}\:\mathrm{f}\left(\mathrm{75}\right)\:\mathrm{is} \\ $$ Answered by 433 last updated on 31/Jul/17 $$ \\ $$$$ \\…
Question Number 18653 by Tinkutara last updated on 26/Jul/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{inequality},\:\mid{x}\:−\:\mathrm{1}\mid\:+\:\mid{x}\:+\:\mathrm{1}\mid\:<\:\mathrm{4} \\ $$ Answered by ajfour last updated on 26/Jul/17 $$\mathrm{If}\:\mathrm{x}<−\mathrm{1} \\ $$$$−\left(\mathrm{x}−\mathrm{1}\right)−\left(\mathrm{x}+\mathrm{1}\right)<\mathrm{4} \\ $$$$\Rightarrow\:\mathrm{2x}>−\mathrm{4}\:\:\mathrm{or}\:\:\mathrm{x}>\:−\mathrm{2} \\…
Question Number 18575 by Tinkutara last updated on 25/Jul/17 $$\mathrm{If}\:\left(\:\right)\:\mathrm{represents}\:\mathrm{the}\:\mathrm{least}\:\mathrm{integer}\:\mathrm{function}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{10}\right)\:+\:\left(\mathrm{10}\:+\:\frac{\mathrm{1}}{\mathrm{20}}\right)\:+ \\ $$$$\left(\mathrm{10}\:+\:\frac{\mathrm{2}}{\mathrm{20}}\right)\:+\:…\:+\:\left(\mathrm{10}\:+\:\frac{\mathrm{19}}{\mathrm{20}}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{219} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{200} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{220} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{221} \\ $$ Answered…