Question Number 2548 by Filup last updated on 22/Nov/15 $$\mathrm{For}\:\mathrm{a}\:\mathrm{function}\:{y}={f}\left({x}\right), \\ $$$$\mathrm{inflection}\:\mathrm{points}/\mathrm{stationary}\:\mathrm{points}\:\mathrm{are} \\ $$$$\mathrm{when}\:\:\frac{{df}}{{dx}}=\mathrm{0}. \\ $$$$ \\ $$$$\mathrm{For}\:\mathrm{a}\:\mathrm{function}\:{z}={f}\left({x},\:{y}\right),\:\mathrm{can}\:\mathrm{you}\:\mathrm{find} \\ $$$$\mathrm{these}\:\mathrm{points}\:\mathrm{through}\:\mathrm{a}\:\mathrm{similar}\:\mathrm{method}? \\ $$$$ \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{something}\:\mathrm{like}\:\frac{\partial{f}}{\partial{x}}=\mathrm{0}\:\mathrm{and}\:\frac{\partial{f}}{\partial{y}}=\mathrm{0}? \\…
Question Number 133616 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{Suppose}\:\mathrm{function}\:\mathrm{f}:\mathrm{R}\rightarrow\mathrm{R}\:\mathrm{with} \\ $$$$\mathrm{f}\left(\mathrm{2x}−\mathrm{3}\right)\:=\:\mathrm{4x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{5}\:\mathrm{and}\:\mathrm{f}\:'\:\mathrm{denote} \\ $$$$\mathrm{is}\:\mathrm{derivatif}\:\mathrm{of}\:\mathrm{f}\:\mathrm{function}. \\ $$$$\mathrm{What}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\:'\left(\mathrm{2x}−\mathrm{3}\right) \\ $$ Commented by mr W last updated…
Question Number 2546 by Rasheed Soomro last updated on 22/Nov/15 $$\boldsymbol{\mathrm{If}}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{matrices}\:\mathrm{of}\:\mathrm{suitable}\:\mathrm{order} \\ $$$$\mathrm{does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{definition}\:\mathrm{for}\:\mathrm{A}^{\mathrm{B}} \:? \\ $$ Commented by Yozzi last updated on 22/Nov/15 $${A}^{{B}} ={e}^{\left({lnA}\right){B}}…
Question Number 2545 by Rasheed Soomro last updated on 22/Nov/15 $$\mathcal{P}{rove}\:{that}\:\mathrm{3}^{\mathrm{3}{n}} −\mathrm{26}{n}−\mathrm{1}\:{is}\:{divisible}\:{by}\:\mathrm{676}, \\ $$$${where}\:{n}\in\mathbb{Z}^{+} \\ $$ Commented by Yozzi last updated on 22/Nov/15 $${Use}\:{induction}. \\…
Question Number 2544 by Rasheed Soomro last updated on 22/Nov/15 $$\mathcal{C}{an}\:{you}\:\mathcal{G}{eneralize}\:{the}\:{following}? \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}=\frac{\mathrm{1}}{\mathrm{2}}\left({n}\right)\left({n}+\mathrm{1}\right) \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +…+{n}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{6}}\left({n}\right)\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right. \\ $$$$\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +…+{n}^{\mathrm{3}} =\left[\frac{\mathrm{1}}{\mathrm{2}}\left({n}\right)\left({n}+\mathrm{1}\right)\right]^{\mathrm{2}}…
Question Number 68078 by anaplak last updated on 04/Sep/19 Answered by Smail last updated on 04/Sep/19 $${C}+{iS}=\mathrm{1}+{z}\left({cos}\theta+{isin}\theta\right)+\frac{{z}^{\mathrm{2}} }{\mathrm{2}!}\left({cos}\mathrm{2}\theta+{isin}\mathrm{2}\theta\right)+… \\ $$$$=\mathrm{1}+{ze}^{{i}\theta} +\frac{\left({ze}^{{i}\theta} \right)^{\mathrm{2}} }{\mathrm{2}!}+…={e}^{{ze}^{{i}\theta} } ={e}^{{zcos}\theta}…
Question Number 133612 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{If}\:\begin{cases}{\mathrm{x}+\mathrm{y}+\mathrm{2z}=\mathrm{k}}\\{\mathrm{x}+\mathrm{2y}+\mathrm{z}=\mathrm{k}}\\{\mathrm{2x}+\mathrm{y}+\mathrm{z}=\mathrm{k}}\end{cases}\:;\:\mathrm{k}\neq\:\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:=? \\ $$$$ \\ $$ Commented by mr W last updated…
Question Number 68079 by azizullah last updated on 04/Sep/19 Answered by Rasheed.Sindhi last updated on 07/Sep/19 $$\begin{pmatrix}{}&{\mathrm{son}'\mathrm{s}\:\mathrm{age}}&{\mathrm{father}'\mathrm{s}\:\mathrm{age}}\\{\mathrm{Now}}&{\:\:\:\:\:\:\:\:\:\:\mathrm{x}}&{\:\:\:\:\:\:\mathrm{x}+\mathrm{36}}\\{\mathrm{10}\:\mathrm{years}\:\mathrm{ago}}&{\:\:\:\:\:\:\mathrm{x}−\mathrm{10}}&{\:\:\:\:\:\:\mathrm{x}+\mathrm{26}}\end{pmatrix}\: \\ $$$$ \\ $$$$\:\:\:\:\mathrm{x}+\mathrm{26}=\mathrm{3}\left(\mathrm{x}−\mathrm{10}\right) \\ $$$$\left.\:\:\:\:\mathrm{x}+\mathrm{26}=\mathrm{3x}−\mathrm{30}\right) \\ $$$$\:\:\:\mathrm{2x}=\mathrm{26}+\mathrm{30}=\mathrm{56}…
Question Number 133615 by benjo_mathlover last updated on 23/Feb/21 $$\mathrm{If}\:\mathrm{log}\:_{\mathrm{4}} \left(\mathrm{log}\:_{\mathrm{2}} \:\mathrm{x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{log}\:_{\mathrm{4}} \:\mathrm{x}\right)=\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{log}\:_{\mathrm{5}} \:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}\:+\mathrm{5}}\:=\:? \\ $$ Answered by TheSupreme last updated on…
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