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Author: Tinku Tara

Given-f-x-2-x-2-x-2-x-2-If-g-f-x-2x-1-then-g-1-1-

Question Number 139592 by bemath last updated on 29/Apr/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}} −\mathrm{x}}\:+\sqrt{\mathrm{2}−\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{If}\:\left(\mathrm{g}\circ\mathrm{f}\right)\left(\mathrm{x}\right)\:=\:\mathrm{2x}+\mathrm{1}\:\mathrm{then}\:\mathrm{g}^{−\mathrm{1}} \left(−\mathrm{1}\right)=? \\ $$ Answered by EDWIN88 last updated on 29/Apr/21 $$\Rightarrow\left(\mathrm{g}\circ\mathrm{f}\right)\left(\mathrm{x}\right)=\:\mathrm{2x}+\mathrm{1}\:;\:\mathrm{g}^{−\mathrm{1}}…

If-a-b-and-c-are-integers-not-all-simultaneously-equal-and-w-1-is-a-cube-root-of-unity-then-the-minimum-value-of-a-bw-cw-2-is-A-0-B-1-C-3-2-D-1-2-

Question Number 139590 by EnterUsername last updated on 29/Apr/21 $$\mathrm{If}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{integers}\:\mathrm{not}\:\mathrm{all}\:\mathrm{simultaneously}\:\mathrm{equal} \\ $$$$\mathrm{and}\:{w}\neq\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{then}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mid{a}+{bw}+{cw}^{\mathrm{2}} \mid\:\mathrm{is}\: \\ $$$$\left(\mathrm{A}\right)\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\sqrt{\mathrm{3}}/\mathrm{2}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{1}/\mathrm{2} \\ $$ Answered by MJS_new last updated on…

Question-8516

Question Number 8516 by Chantria last updated on 14/Oct/16 Commented by 123456 last updated on 14/Oct/16 $$\:{aa}+{bb}+{cc}={abc} \\ $$$$\mathrm{11}\left({a}+{b}+{c}\right)=\mathrm{100}{a}+\mathrm{10}{b}+{c} \\ $$$$\mathrm{11}{a}+\mathrm{11}{b}+\mathrm{11}{c}=\mathrm{100}{a}+\mathrm{10}{b}+{c} \\ $$$${b}+\mathrm{10}{c}=\mathrm{89}{a} \\ $$…

show-that-0-1-x-2-1-x-4-dx-1-4-3-4-1-2-

Question Number 8514 by Basant007 last updated on 14/Oct/16 $$\mathrm{show}\:\mathrm{that}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{4}}\beta\left(\frac{\mathrm{3}}{\mathrm{4}},\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Commented by swapnil last updated on 18/Oct/16 $$\mathrm{what}\:\mathrm{is}\:\beta\:\mathrm{here} \\…

Question-139587

Question Number 139587 by mathlove last updated on 29/Apr/21 Answered by qaz last updated on 29/Apr/21 $${f}\left(\mathrm{2}\right)=\int_{\mathrm{1}} ^{\mathrm{2}} {x}^{\mathrm{2}} +\mathrm{3}{xdx}+{f}\left(\mathrm{1}\right)=\left(\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{3}}{\mathrm{2}}{x}^{\mathrm{2}} \right)\mid_{\mathrm{1}} ^{\mathrm{2}} +\mathrm{5}=\frac{\mathrm{71}}{\mathrm{6}} \\…