Question Number 67684 by Rio Michael last updated on 30/Aug/19 $${given}\:{the}\:{function}\: \\ $$$${f}\left({x}\right)\:=\begin{cases}{{x}^{\mathrm{2}} \:\:,\:{for}\:\:\:\mathrm{0}\leqslant\:{x}<\:\mathrm{2}}\\{{ax}\:+\:\mathrm{3},\:{for}\:\:\mathrm{2}\leqslant\:{x}\:<\:\mathrm{4}}\end{cases} \\ $$$${is}\:{periodic}\:{of}\:{period}\:\:\mathrm{4},\:{and}\:{is}\:{continuous}. \\ $$$$\left.{a}\right)\:{Find}\:\:{the}\:{value}\:{of}\:\:{a}. \\ $$$$\left.{b}\right)\:{Find}\:{the}\:{valu}\:{of}\:\:{f}\left(\mathrm{6}\right) \\ $$$$\left.{c}\right)\:{sketch}\:{the}\:{graph}\:{for}\:{y}\:={f}\left({x}\right). \\ $$$${help}\:{me}\:{please},\:{for}\:{the}\:{graph}\:{i}\:{don}'{t}\:{know}\:{wbere}\:{to}\:{put}\:\:{y}={x}^{\mathrm{2}} \:{and}\:{y}\:=\:{ax}\:+\:\mathrm{3}\:{and}…
Question Number 67687 by Rio Michael last updated on 30/Aug/19 $${find}\:{the}\:{range}\:{of}\:{values}\:{of}\: \\ $$$$\:\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{9}}{\mathrm{3}_{\:} }\mid=\:\frac{\mathrm{9}−{x}^{\mathrm{2}} }{\mathrm{3}} \\ $$$$ \\ $$ Commented by mr W last…
Question Number 67664 by Rio Michael last updated on 29/Aug/19 $${show}\:{that}\:\:\exists\:{n}\:\in\:{N}^{+\:} \::\:\:{sin}^{{n}} {x}\:+\:{cos}^{{n}} {x}\:=\:\mathrm{1}\:{and}\:\:{cosh}^{{n}} {x}\:−\:{sinh}^{{n}} {x}\:=\:\mathrm{1}. \\ $$$$ \\ $$$${Hint}:\:{use}\:{Induction}\:{method}. \\ $$$$ \\ $$ Commented…
Question Number 67662 by Rio Michael last updated on 29/Aug/19 $${please}\:{explain}\:{the}\:{fact}\:{that}\: \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx}\:=\:{ln}\:{x}\:+\:{k} \\ $$ Commented by malwaan last updated on 29/Aug/19 $$\int\frac{{f}\:'\left({x}\right)}{{f}\left({x}\right)}{dx}\:={ln}\:\mid{f}\left({x}\right)\mid+\:{c} \\ $$$$\left({x}\right)'=\mathrm{1}…
Question Number 67659 by Rio Michael last updated on 29/Aug/19 $${Help}\:{me}\:{obtain}\:\:\:{the}\:{value}\:{of}\:\:{e}\:{from} \\ $$$$\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{n}}\right)^{{n}} \:\:{how}\:{do}\:{i}\:{go}\:{about}\:{it}. \\ $$ Commented by Abdo msup. last updated on 30/Aug/19 $${A}_{{n}}…
Question Number 2111 by 123456 last updated on 03/Nov/15 $$\mathrm{lets}\:{f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{does} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial}{\partial{x}}\underset{\mathrm{0}} {\overset{{x}} {\int}}\frac{\partial{f}}{\partial{y}}{dy}\:\:\:? \\ $$ Answered by prakash jain last updated…
Question Number 67631 by Hassen_Timol last updated on 29/Aug/19 $$ \\ $$$$ \\ $$$$\:\:\:\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{me},\:\mathrm{where}\:\mathrm{does}\:\mathrm{this}\: \\ $$$$\:\:\:\mathrm{formula}\:\mathrm{come}\:\mathrm{from}? \\ $$$$\:\:\:\mathrm{And}\:\mathrm{what}\:\mathrm{means}\:\mathrm{the}\:\mathrm{factorial}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}- \\ $$$$\:\:\:\mathrm{integer}\:\mathrm{number}? \\ $$$$ \\ $$$$\:\:\:\:\:\:\pi\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}!\right)^{\mathrm{2}} ×\:\mathrm{4}…
Question Number 2075 by 123456 last updated on 01/Nov/15 $${f}^{−\mathrm{1}} \left({x}\right)={f}'\left({x}\right) \\ $$$${f}\left({x}\right)=?? \\ $$ Commented by Yozzi last updated on 01/Nov/15 $$\mathrm{1}={f}\left({x}\right){f}^{'} \left({x}\right) \\…
Question Number 133103 by 777316 last updated on 18/Feb/21 Commented by bemath last updated on 18/Feb/21 $$\mathrm{If}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{c}\:\mathrm{then}\:\mathrm{ln}\:\mathrm{x}+\mathrm{ln}\:\mathrm{y}\:\neq\:\mathrm{ln}\:\mathrm{c}\: \\ $$$$\mathrm{sir}\: \\ $$ Commented by malwan last…
Question Number 133069 by Dwaipayan Shikari last updated on 18/Feb/21 Commented by Dwaipayan Shikari last updated on 18/Feb/21 $${One}\:{can}\:{stretch}\:{and}\:{reform}\:{sides}\:{AB}\:\:{and}\:{AC}\:,\:{by}\: \\ $$$${considering}\:{length}\:\:{BC}\:{as}\:{constant}.\:{the}\:{angle}\: \\ $$$$\phi\:{can}\:{change}.\:{Find}\:{the}\:{relationship}\:{of}\:{changes}\:{between}\:{Side}\: \\ $$$${AB}\:,\:{AC}\:{and}\:{angle}\:\phi…