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…
Question Number 83956 by jagoll last updated on 08/Mar/20 $$\mathrm{for}\:\mathrm{x}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{3x}\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{2019}\right)\:.\: \\ $$ Commented by mr W last updated on 08/Mar/20 $$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{3x}\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right)\:\:\:…\left({i}\right)…
Question Number 18416 by Tinkutara last updated on 20/Jul/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{which}\:\mathrm{satisfies} \\ $$$$\frac{\left({x}\:−\:\mathrm{5}\right)^{\mathrm{10}} \left({x}\:−\:\mathrm{13}\right)^{\mathrm{20}} \left({x}\:−\:\mathrm{19}\right)^{\mathrm{13}} }{\left({x}\:−\:\mathrm{10}\right)^{\mathrm{18}} \left({x}\:−\:\mathrm{25}\right)^{\mathrm{19}} }\:\geqslant\:\mathrm{0}\:\mathrm{and} \\ $$$$\mathrm{2}\:\leqslant\:{x}\:\leqslant\:\mathrm{30}\:\mathrm{are} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{23} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{24}…
Question Number 18333 by ajfour last updated on 19/Jul/17 Commented by ajfour last updated on 19/Jul/17 $$\mathrm{In}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Q}.\mathrm{18327} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 83662 by jagoll last updated on 05/Mar/20 $$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{3}}} \\ $$$$\mathrm{find}\:\mathrm{domain}\:\mathrm{function}\: \\ $$$$\left(\mathrm{g}\:\bullet\:\mathrm{f}\right)\left(\mathrm{x}\right) \\ $$ Commented by MJS last updated on 05/Mar/20…
Question Number 83610 by john santu last updated on 04/Mar/20 $$\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}\:+\:\frac{\mathrm{5}}{\mathrm{6}−\mathrm{3}\sqrt{\mathrm{6}+\mathrm{x}−\mathrm{x}^{\mathrm{2}} }}\:>\:\frac{\mathrm{1}}{\mathrm{1}+\mid\mathrm{x}−\mathrm{1}\mid} \\ $$ Commented by john santu last updated on 04/Mar/20 $$\mathrm{ans}\::\:\left[−\mathrm{2},\:−\mathrm{1}\right)\:\cup\:\left(\mathrm{1},\:\frac{\mathrm{6}}{\mathrm{5}}\right)\:\cup\:\left(\mathrm{2},\mathrm{3}\:\right] \\ $$…
Question Number 83539 by jagoll last updated on 03/Mar/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}? \\ $$ Commented by john santu last updated on 03/Mar/20 $$\mathrm{domain}\:\mathrm{x}^{\mathrm{2}} −\mathrm{1}>\mathrm{0}\:\Rightarrow\:\mathrm{x}<−\mathrm{1}\:\vee\mathrm{x}\:>\mathrm{1}…