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…
Question Number 18574 by Tinkutara last updated on 25/Jul/17 $$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\mathrm{2}\:−\:\mid{x}\mid^{\mathrm{2}} \\ $$$$−\:\mathrm{2}{x}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{3} \\ $$ Answered by prakash…
Question Number 84029 by mathmax by abdo last updated on 08/Mar/20 $${let}\:{f}\left({x}\right)={e}^{−{nx}} {ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right){find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){d}\:{and}\:\int_{\mathrm{0}} ^{\infty}…
Question Number 149551 by puissant last updated on 06/Aug/21 Answered by Olaf_Thorendsen last updated on 06/Aug/21 $${a}_{{n}} \:=\:\mathrm{P}\left({n}\right)\:=\:{an}^{\mathrm{2}} +{bn}+{c} \\ $$$$\forall{n}\in\mathbb{N},\:{a}_{{n}+\mathrm{1}} \:=\:\mathrm{3}{a}_{{n}} −{n}^{\mathrm{2}} +{n} \\…
Question Number 83977 by john santu last updated on 08/Mar/20 $$\mathrm{find}\:\mathrm{range}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{x}\sqrt{\mathrm{7x}−\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\mathrm{without} \\ $$$$\mathrm{calculus} \\ $$ Answered by john santu last updated on…