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Question-146886

Question Number 146886 by Khalmohmmad last updated on 16/Jul/21 Commented by EDWIN88 last updated on 16/Jul/21 $$!\mathrm{n}\:=\mathrm{n}!\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{k}!} \\ $$$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{!\mathrm{n}}{\mathrm{n}!}\:=\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{n}!\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}}…

Given-4-x-4-x-2-2-x-2-2-x-7-0-x-gt-0-find-2-x-2-x-if-x-pi-6-0-then-minimum-value-of-function-f-x-cot-x-pi-3-tan-2pi-3-x-when-x-

Question Number 146838 by bobhans last updated on 16/Jul/21 $$\mathrm{Given}\:\mathrm{4}^{\mathrm{x}} +\mathrm{4}^{−\mathrm{x}} −\mathrm{2}^{\mathrm{2}−\mathrm{x}} +\mathrm{2}^{\mathrm{2}+\mathrm{x}} −\mathrm{7}=\mathrm{0}\:,\mathrm{x}>\mathrm{0} \\ $$$$\:\mathrm{find}\:\mathrm{2}^{\mathrm{x}} +\mathrm{2}^{−\mathrm{x}} . \\ $$$$\: \\ $$$$\:\mathrm{if}\:\mathrm{x}\in\left[\:−\frac{\pi}{\mathrm{6}},\mathrm{0}\:\right]\:\mathrm{then}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{cot}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{3}}\right)−\mathrm{tan}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\right)\: \\…

p-is-a-point-inside-onside-outside-of-equilateral-triangle-find-side-of-triangle-if-distance-of-p-from-vertices-of-triangle-be-equail-to-5-7-11-study-each-conditions-separately-find-side-of-A

Question Number 81267 by behi83417@gmail.com last updated on 10/Feb/20 $$\boldsymbol{\mathrm{p}},\mathrm{is}\:\mathrm{a}\:\mathrm{point},\boldsymbol{\mathrm{inside}}\:,\boldsymbol{\mathrm{onside}}\:,\boldsymbol{\mathrm{outside}}\:\mathrm{of} \\ $$$$\mathrm{equilateral}\:\mathrm{triangle}.\mathrm{find}\:\mathrm{side}\:\mathrm{of}\:\mathrm{triangle} \\ $$$$\mathrm{if}\:\mathrm{distance}\:\mathrm{of}\::\boldsymbol{\mathrm{p}}\:\mathrm{from}\:\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{triangle} \\ $$$$\mathrm{be}\:\mathrm{equail}\:\mathrm{to}:\:\mathrm{5},\mathrm{7},\mathrm{11}. \\ $$$$\left(\mathrm{study}\:\mathrm{each}\:\mathrm{conditions}\:\mathrm{separately}\right). \\ $$$$\mathrm{find}\:\mathrm{side}\:\mathrm{of}\:\mathrm{ABC}\:\mathrm{and}\:\mathrm{p}_{\mathrm{1}} \mathrm{p}_{\mathrm{2}} \mathrm{p}_{\mathrm{3}} \:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{special}\:\mathrm{case}\:\mathrm{that}:\begin{cases}{\mathrm{Ap}_{\mathrm{1}}…