Menu Close

Author: Tinku Tara

f-x-f-y-2-f-x-y-2-x-y-R-f-x-

Question Number 1668 by 123456 last updated on 30/Aug/15 $$\frac{{f}\left({x}\right)+{f}\left({y}\right)}{\mathrm{2}}={f}\left(\frac{{x}+{y}}{\mathrm{2}}\right),\forall{x},{y}\in\mathbb{R} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Rasheed Ahmad last updated on 30/Aug/15 $${f}\left({x}\right)\:{has}\:{two}\:{properties}: \\ $$$$\left(\mathrm{1}\right)\:{f}\left({cx}\right)={cf}\left({x}\right)\:{for}\:{constant}\:{c}…

Question-67193

Question Number 67193 by Rasheed.Sindhi last updated on 23/Aug/19 Commented by Rasheed.Sindhi last updated on 24/Aug/19 $$\:\underset{−} {\:\:\:\:\:\:\:\:\:\:\mathbb{S}\mathrm{ome}\:\mathbb{C}\mathrm{ounting}\:\mathbb{P}\mathrm{roblems}\:\:\:\:\:\:\:\:\:\:} \\ $$$$\left({a}\right){How}\:{many}\:{rectangles}\:{are}\:{in}\:{the} \\ $$$$\:\:\:\:\:\:\:{above}\:{picture}? \\ $$$$\left({b}\right){How}\:{many}\:{rectangles}\:{contain} \\…

Let-A-B-and-C-are-three-statments-A-B-C-A-C-B-A-B-C-A-B-A-Prove-or-disprove-

Question Number 1656 by Rasheed Soomro last updated on 29/Aug/15 $$\mathrm{Let}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{three}\:\mathrm{statments}.\: \\ $$$$\left(\mathrm{A}\Rightarrow\mathrm{B}\Rightarrow\mathrm{C}\Rightarrow\mathrm{A}\right)\:\overset{?} {\Rightarrow}\left(\mathrm{C}\Rightarrow\mathrm{B}\right)\: \\ $$$$\left(\mathrm{A}\Rightarrow\mathrm{B}\Rightarrow\mathrm{C}\Rightarrow\mathrm{A}\right)\:\overset{?} {\Rightarrow}\left(\mathrm{B}\Rightarrow\mathrm{A}\right)\: \\ $$$$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}. \\ $$ Commented by Yozzian last…

solve-inside-R-3-the-system-2x-y-z-1-x-2y-z-2-x-y-2z-3-

Question Number 67189 by mathmax by abdo last updated on 23/Aug/19 $${solve}\:{inside}\:{R}^{\mathrm{3}} \:{the}\:{system}\:\begin{cases}{\mathrm{2}{x}+{y}+{z}\:=\mathrm{1}}\\{{x}+\mathrm{2}{y}+{z}\:=\mathrm{2}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{x}+{y}+\mathrm{2}{z}\:=\mathrm{3}\right. \\ $$ Answered by MJS last updated on 23/Aug/19 $${D}=\begin{vmatrix}{\mathrm{2}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{2}}\end{vmatrix}=\mathrm{4}…

let-f-x-arctan-x-3-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-3-calculate-0-1-arctan-x-3-dx-

Question Number 67187 by mathmax by abdo last updated on 23/Aug/19 $${let}\:{f}\left({x}\right)\:={arctan}\left({x}^{\mathrm{3}} \right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right){and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{\mathrm{3}} \right){dx} \\…

Calculate-I-a-b-0-1-t-a-1-t-b-dt-given-that-I-a-b-b-a-1-I-a-1-b-1-a-gt-0-b-gt-0-Use-the-fact-that-I-a-b-I-a-1-b-I-a-b-1-and-I-a-b-I-b-a-to-help-evaluate-I-a-b-

Question Number 1643 by 112358 last updated on 28/Aug/15 $${Calculate}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{{a}} \left(\mathrm{1}−{t}\right)^{{b}} {dt} \\ $$$${given}\:{that}\:{I}\left({a},{b}\right)=\frac{{b}}{{a}+\mathrm{1}}{I}\left({a}+\mathrm{1},{b}−\mathrm{1}\right) \\ $$$$\left({a}>\mathrm{0},{b}>\mathrm{0}\right).\:{Use}\:{the}\:{fact}\:{that} \\ $$$${I}\left({a},{b}\right)={I}\left({a}+\mathrm{1},{b}\right)+{I}\left({a},{b}+\mathrm{1}\right) \\ $$$${and}\:{I}\left({a},{b}\right)={I}\left({b},{a}\right)\: \\…