Category: Relation and Functions

Question Number 16457 by Tinkutara last updated on 22/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\frac{\mathrm{3}}{\mathrm{2}\:−\:{x}^{\mathrm{2}} } \\ $$ Answered by sandy_suhendra last updated on 22/Jun/17 $$\mathrm{y}\:=\:\frac{\mathrm{3}}{\mathrm{2}−\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{y}\left(\mathrm{2}−\mathrm{x}^{\mathrm{2}} \right)=\mathrm{3}…

Question Number 147466 by mathmax by abdo last updated on 21/Jul/21 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{5} \\ $$$$\mathrm{find}\:\int\:\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)}\mathrm{dx}\:\:\:\mathrm{and}\:\int\:\:\frac{\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{x}\right)}\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on…

Question Number 147302 by puissant last updated on 19/Jul/21 $${P}_{{a}} \left({z}\right)={z}^{\mathrm{2}{n}} −\mathrm{2}{z}^{{n}} {cosa}+\mathrm{1} \\ $$$${montrer}\:{que}\:\:{p}_{{a}} \left(\mathrm{z}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({z}^{\mathrm{2}} −\mathrm{2}{zcos}\left(\frac{{a}}{\pi}+\frac{\mathrm{2}{k}\pi}{{n}}\right)+\mathrm{1}\right) \\ $$ Answered by mathmax by…

Question Number 81720 by mathmax by abdo last updated on 14/Feb/20 $${let}\:{f}\left({x}\right)={arctan}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developpf}\:{at}\:{integr}\:{serie} \\ $$ Commented by mathmax by…

Question Number 147205 by mathmax by abdo last updated on 18/Jul/21 $$\mathrm{calculate}\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{arctan}\left(\frac{\mathrm{3}}{\mathrm{x}}\right)}{\mathrm{2x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on…