Menu Close

Author: Tinku Tara

Question-6436

Question Number 6436 by sanusihammed last updated on 27/Jun/16 Answered by Rasheed Soomro last updated on 28/Jun/16 $${P}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +{ax}+{b} \\ $$$${x}−\mathrm{2}\:{is}\:{factor}\:{of}\:{P}\left({x}\right)\:{means}\:{if}\:{P}\left({x}\right)\:{is}\:{divided} \\ $$$${by}\:{x}−\mathrm{2}\:,\:{the}\:{remainder}\:{will}\:{be}\:\mathrm{0} \\…

advanced-calculus-prove-that-0-1-ln-x-ln-1-x-1-x-dx-13-8-3-pi-2-4-ln-2-

Question Number 137501 by mnjuly1970 last updated on 03/Apr/21 $$\:\:\:\:\:\:\:….{advanced}\:….\:{calculus}…. \\ $$$$\:\:{prove}\:{that}:: \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}}{dx}=\frac{\mathrm{13}}{\mathrm{8}}\zeta\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{2}} }{\mathrm{4}}{ln}\left(\mathrm{2}\right)…. \\ $$ Answered by Ñï= last updated on…

An-oil-can-is-to-be-made-in-form-of-a-right-circular-cylinder-that-be-inscribed-in-a-sphere-of-radius-R-obtain-the-maximum-volume-of-the-can-

Question Number 6430 by sanusihammed last updated on 27/Jun/16 $${An}\:{oil}\:{can}\:{is}\:{to}\:{be}\:{made}\:{in}\:{form}\:{of}\:{a}\:{right}\:{circular}\:{cylinder}\:{that}\:{be} \\ $$$${inscribed}\:{in}\:{a}\:{sphere}\:{of}\:{radius}\:{R}.\:{obtain}\:{the}\:{maximum}\: \\ $$$${volume}\:{of}\:{the}\:{can}. \\ $$ Commented by sanusihammed last updated on 27/Jun/16 $${Thanks}\:{so}\:{much}\:{sir}.\: \\…

Question-71960

Question Number 71960 by TawaTawa last updated on 22/Oct/19 Answered by mind is power last updated on 22/Oct/19 $$\Sigma\frac{\mathrm{1}+\mathrm{a}}{\mathrm{1}−\mathrm{a}}=\Sigma\left(−\mathrm{1}+\frac{\mathrm{2}}{\mathrm{1}−\mathrm{a}}\right)=\Sigma−\mathrm{1}+\Sigma\frac{\mathrm{2}}{\mathrm{1}−\mathrm{a}} \\ $$$$\frac{\mathrm{p}'\left(\mathrm{x}\right)}{\mathrm{p}\left(\mathrm{x}\right)}=\underset{\mathrm{a}\in\mathrm{Root}\left(\mathrm{p}\right)} {\sum}\frac{\mathrm{1}}{\mathrm{x}−\mathrm{a}} \\ $$$$\Rightarrow\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{3}}…

Convert-34-8989898989-and-0-789789789789-to-fraction-

Question Number 6419 by sanusihammed last updated on 26/Jun/16 $${Convert}\:\:\:\:\mathrm{34}.\mathrm{8989898989}\:\:\:\:{and}\:\:\:\:\mathrm{0}.\mathrm{789789789789}\: \\ $$$${to}\:{fraction}. \\ $$ Answered by Rasheed Soomro last updated on 26/Jun/16 $${Do}\:{you}\:{mean}\:\:\mathrm{34}.\mathrm{8989898989}…\:\mathrm{89}\:{forever} \\ $$$${and}\:\mathrm{0}.\mathrm{789789789789}…\mathrm{789}\:{forever}?…

y-t-C-v-t-y-t-1-v-t-t-Here-t-is-the-variable-y-t-is-the-function-y-t-is-its-first-derivative-v-t-is-an-another-function-in-the-same-variable-t-C-is-a-constant-Find-an-

Question Number 6415 by sanusihammed last updated on 26/Jun/16 $${y}^{'} \left({t}\right)\:=\:{C}\:+\:\frac{{v}\left({t}\right){y}\left({t}\right)}{\mathrm{1}\:+\:{v}\left({t}\right){t}} \\ $$$$ \\ $$$${Here},\:{t}\:\:{is}\:{the}\:{variable}\: \\ $$$${y}\left({t}\right)\:{is}\:{the}\:{function} \\ $$$${y}^{'} \left({t}\right)\:{is}\:{its}\:{first}\:{derivative}\: \\ $$$${v}\left({t}\right)\:{is}\:{an}\:{another}\:{function}\:{in}\:{the}\:{same}\:{variable}\:\:{t}\: \\ $$$${C}\:\:{is}\:{a}\:{constant}. \\…