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Author: Tinku Tara

Question-138175

Question Number 138175 by ajfour last updated on 10/Apr/21 Commented by ajfour last updated on 10/Apr/21 $${If}\:{the}\:{yellow}\:{and}\:{blue}\:{areas}\:{are} \\ $$$${equal},\:{find}\:{edge}\:{length}\:{of}\:{the} \\ $$$${blue}\:{square}.\:\left({radius}\:{of}\:{circle}=\mathrm{1}\right) \\ $$ Answered by…

help-me-with-the-conditions-please-for-a-function-f-to-be-continuous-at-a-point-a-

Question Number 72634 by Rio Michael last updated on 30/Oct/19 $${help}\:{me}\:{with}\:{the}\:{conditions}\:{please}\: \\ $$$${for}\:{a}\:{function}\:{f}\:{to}\:{be}\:{continuous}\:{at}\:{a}\:{point}\:{a} \\ $$ Commented by Prithwish sen last updated on 31/Oct/19 $$\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{able}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{draw}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{function}}\:\boldsymbol{\mathrm{f}}\:\:\boldsymbol{\mathrm{through}} \\…

mathematical-analysis-if-0-1-arctan-x-ln-1-x-2-x-2-dx-1-48-api-2-bpiln-2-c-ln-2-2-then-a-2-b-c-1-2-

Question Number 138171 by mnjuly1970 last updated on 11/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:…….{mathematical}….{analysis}……. \\ $$$$\:\:\:\:\:{if}\::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{48}}\left({a}\pi^{\mathrm{2}} −{b}\pi{ln}\left(\mathrm{2}\right)+{c}\:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:……{then}\:\:….\:{a}^{\mathrm{2}} +\left({b}−{c}+\mathrm{1}\right)^{\mathrm{2}} =??? \\…

Question-7096

Question Number 7096 by Tawakalitu. last updated on 10/Aug/16 Commented by Rasheed Soomro last updated on 10/Aug/16 $${First}\:{vertex}\:{of}\:{a}\:{triangle}\:{can}\:{be} \\ $$$${chosen}\:{in}\:{n}\:{ways}\:{in}\:{a}\:{regular}\:{n}-{gon}. \\ $$$${The}\:{second}\:{vertex}\:{can}\:{be}\:{chosen}\:{in} \\ $$$${n}−\mathrm{1}\:{ways}.\:{The}\:{third}\:{vertex}\:{can}\:{be}\: \\…

If-we-have-a-vector-v-x-y-and-apply-a-linear-tranformation-such-that-a-new-vector-v-x-y-is-made-can-we-calculate-the-change-of-area-with-respect-to-the-unit-vector-

Question Number 7093 by FilupSmith last updated on 10/Aug/16 $$\mathrm{If}\:\mathrm{we}\:\mathrm{have}\:\mathrm{a}\:\mathrm{vector}\:\boldsymbol{{v}}=\begin{bmatrix}{{x}}\\{{y}}\end{bmatrix} \\ $$$$\mathrm{and}\:\mathrm{apply}\:\mathrm{a}\:\mathrm{linear}\:\mathrm{tranformation}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{vector}\:\boldsymbol{{v}}^{'} =\begin{bmatrix}{{x}'}\\{{y}'}\end{bmatrix}\:\mathrm{is}\:\mathrm{made}, \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{change}\:\mathrm{of}\:\mathrm{area}\:\mathrm{with} \\ $$$$\mathrm{respect}\:\mathrm{to}\:\mathrm{the}\:\hat {\imath}\:\mathrm{unit}\:\mathrm{vector}? \\ $$ Commented by FilupSmith…