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Author: Tinku Tara

Question-209229

Question Number 209229 by Tawa11 last updated on 04/Jul/24 Commented by klipto last updated on 06/Jul/24 $$\boldsymbol{\mathrm{take}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{both}}\:\boldsymbol{\mathrm{side}} \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{iny}}=\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{inx}} \\ $$$$\frac{\boldsymbol{\mathrm{d}}\left(\boldsymbol{\mathrm{iny}}\right)}{\boldsymbol{\mathrm{dx}}}=\boldsymbol{\mathrm{v}}\frac{\boldsymbol{\mathrm{du}}}{\boldsymbol{\mathrm{dx}}}+\boldsymbol{\mathrm{u}}\frac{\boldsymbol{\mathrm{dv}}}{\boldsymbol{\mathrm{dx}}} \\ $$$$\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{inx}}+\frac{\mathrm{e}^{\mathrm{x}}…

Question-209220

Question Number 209220 by alcohol last updated on 04/Jul/24 Answered by Berbere last updated on 04/Jul/24 $${SAB}\:,{SAC}\:\:\&{ABC}\:{c}\:{est}\:{claire}\:\left({AS}\right)\bot\left({ABC}\right)\:\&{ABC}\:{rectangle} \\ $$$$\Rightarrow{SA}^{\mathrm{2}} +{AB}^{\mathrm{2}} ={SB}^{\mathrm{2}} ;{SA}^{\mathrm{2}} +{AC}^{\mathrm{2}} ={SC}^{\mathrm{2}} ;{CA}^{\mathrm{2}}…

u-0-a-u-n-1-u-n-v-n-v-0-b-0-1-v-n-1-1-2-u-n-v-n-show-that-a-u-n-u-n-1-v-n-v-n-1-b-show-that-v-n-u-n-a-b-2-n-

Question Number 209232 by alcohol last updated on 04/Jul/24 $${u}_{\mathrm{0}} \:=\:{a},\:{u}_{{n}+\mathrm{1}} \:=\:\sqrt{{u}_{{n}} {v}_{{n}} } \\ $$$$\left.{v}_{\mathrm{0}} \:=\:{b}\:\in\:\right]\mathrm{0},\mathrm{1}\left[\:,\:{v}_{{n}+\mathrm{1}} \:=\:\frac{\mathrm{1}}{\mathrm{2}\left({u}_{{n}} +{v}_{{n}} \right)}\right. \\ $$$$\bullet\:{show}\:{that}\:{a}\leqslant{u}_{{n}} \leqslant{u}_{{n}+\mathrm{1}} \leqslant{v}_{{n}} \leqslant{v}_{{n}+\mathrm{1}}…

calculate-I-0-tan-1-x-1-x-2-2-dx-

Question Number 209217 by mnjuly1970 last updated on 04/Jul/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{calculate}}\:: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\mathrm{0}\:} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}\:+\:{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\: \\ $$$$ \\ $$…

Arrange-in-descending-order-5-2-7-5-13-11-19-17-

Question Number 209234 by Tawa11 last updated on 04/Jul/24 $$\mathrm{Arrange}\:\mathrm{in}\:\mathrm{descending}\:\mathrm{order}: \\ $$$$\:\:\:\:\sqrt{\mathrm{5}}\:\:−\:\:\sqrt{\mathrm{2}},\:\:\:\:\:\sqrt{\mathrm{7}}\:\:−\:\:\sqrt{\mathrm{5}}\:,\:\:\:\sqrt{\mathrm{13}}\:\:−\:\:\sqrt{\mathrm{11}}\:,\:\:\:\sqrt{\mathrm{19}}\:\:−\:\:\sqrt{\mathrm{17}} \\ $$ Answered by A5T last updated on 04/Jul/24 $${Same}\:{arrangement}: \\ $$$$\sqrt{\mathrm{5}}−\sqrt{\mathrm{2}}\left(>\sqrt{\mathrm{5}}−\sqrt{\mathrm{3}}\right)>\sqrt{\mathrm{7}}−\sqrt{\mathrm{5}}>\sqrt{\mathrm{13}}−\sqrt{\mathrm{11}}>\sqrt{\mathrm{19}}−\sqrt{\mathrm{17}} \\…