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Author: Tinku Tara

Question-4219

Question Number 4219 by Yozzii last updated on 02/Jan/16 Answered by prakash jain last updated on 02/Jan/16 $${f}\:'\left(\theta\right)=\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left(\theta+\delta\theta\right)−{f}\left(\theta\right)}{\delta\theta} \\ $$$$\mathrm{If}\:\mathrm{limit}\:\mathrm{exits} \\ $$$$\Rightarrow\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left(\theta+\delta\theta\right)={f}\left(\theta\right)+\underset{\delta\theta\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\:'\left(\theta\right)\delta\theta…

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Question Number 4216 by Rasheed Soomro last updated on 02/Jan/16 $$\boldsymbol{\mathrm{D}}\mathrm{etermine}\:\mathrm{a}\:\mathrm{triplet}\:\left(\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\right)\:\mathrm{of}\:\mathrm{real}\:\mathrm{numbers}\: \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{relation}\:\boldsymbol{\mathrm{a}}^{−\mathrm{1}} +\boldsymbol{\mathrm{b}}^{−\mathrm{1}} =\boldsymbol{\mathrm{c}}^{−\mathrm{1}} \mathrm{and}\:\:\mathrm{satisfying}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{conditions} \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}>\boldsymbol{\mathrm{c}}\:\wedge\:\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}>\boldsymbol{\mathrm{a}}\:\wedge\:\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{a}}>\boldsymbol{\mathrm{b}}\:. \\ $$ Terms of Service…

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Question Number 69738 by Therealsincro last updated on 27/Sep/19 $${Sarah}\:{dances}\:{everyday}\:{of}\:{the}\:{week}, \\ $$$${including}\:{saturdays}\:{and}\:{sundays}. \\ $$$${In}\:{november}\:\mathrm{2018},\:{Sarah}\:{had}\:{to}\:{miss} \\ $$$${a}\:{few}\:{days}.\:{To}\:{control}\:{her}\:{absences} \\ $$$${she}\:{marks}\:{the}\:{day}\:{she}\:{missed}\:{class} \\ $$$${with}\:{a}\:\boldsymbol{{x}}\:{on}\:{the}\:{calendar}. \\ $$$${She}\:{marked}\:{the}\:\mathrm{5}{th},\:\mathrm{21}{st}\:{and}\:\mathrm{27}{th} \\ $$$${of}\:{november}. \\…

I-have-no-formal-background-in-number-theory-but-I-m-curious-of-how-to-find-positive-integer-solutions-x-y-z-to-the-equation-x-n-y-n-z-n-for-n-Z-Fermat-s-last-theorem-led-me-to-this-Tell

Question Number 4203 by Yozzii last updated on 01/Jan/16 $${I}\:{have}\:{no}\:{formal}\:{background}\:{in}\: \\ $$$${number}\:{theory},\:{but}\:{I}'{m}\:{curious} \\ $$$${of}\:{how}\:{to}\:{find}\:{positive}\:{integer}\:{solutions}\: \\ $$$$\left({x},{y},{z}\right)\:{to}\:{the}\:{equation}\:{x}^{{n}} +{y}^{{n}} ={z}^{{n}} \:{for}\: \\ $$$${n}\in\mathbb{Z}^{−} .\:{Fermat}'{s}\:{last}\:{theorem}\:{led} \\ $$$${me}\:{to}\:{this}.\:{Tell}\:{me}\:{about}\:{the}\:{cases} \\…