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Category: Differentiation

Question-152631

Question Number 152631 by mnjuly1970 last updated on 30/Aug/21 Answered by Olaf_Thorendsen last updated on 30/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} +{x}^{\mathrm{4}} \right)}{{x}^{\mathrm{2}} }\:{dx} \\ $$$$\mathrm{I}\:=\:\left[−\frac{\mathrm{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} +{x}^{\mathrm{4}}…

Question-152478

Question Number 152478 by imjagoll last updated on 28/Aug/21 Answered by mr W last updated on 28/Aug/21 $${x}=\mathrm{5}\:\mathrm{cos}\:\theta \\ $$$${y}=\mathrm{5}\:\mathrm{sin}\:\theta \\ $$$${k}=\mathrm{2}×\mathrm{25}\:\mathrm{cos}^{\mathrm{2}} \:\theta+\mathrm{6}×\mathrm{25}\:\mathrm{cos}\:\theta\:\mathrm{sin}\:\theta−\mathrm{4}×\mathrm{25}\:\mathrm{sin}^{\mathrm{2}} \:\theta \\…

prove-that-0-1-x-ln-2-1-x-1-x-2-dx-1-96-ln-2-pi-2-4-ln-2-2-M-N-

Question Number 152350 by mnjuly1970 last updated on 27/Aug/21 $$ \\ $$$$\:\:\:\mathrm{prove}\:\mathrm{that}\:…. \\ $$$$\:\: \\ $$$$\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}.\:{ln}^{\:\mathrm{2}} \left(\:\mathrm{1}+\:{x}\:\right)}{\mathrm{1}\:+\:{x}^{\:\mathrm{2}} }\:\:\:{dx}\:=\frac{\mathrm{1}}{\mathrm{96}}\:{ln}\left(\mathrm{2}\:\right)\:\left(\:\pi^{\:\mathrm{2}} \:+\:\mathrm{4}\:{ln}^{\:\mathrm{2}} \:\left(\mathrm{2}\:\right)\right)….\blacksquare\:\:\:\:\: \\ $$$$\:\:\:\mathrm{M}.\mathrm{N}.. \\…

why-any-infinitely-differentiable-function-is-a-power-series-mathematically-if-f-x-is-A-infinitely-differentiable-function-then-why-f-x-ax-0-bx-1-cx-2-dx-3-ex-4-for-example-sin-x-x-x

Question Number 21270 by Nayon last updated on 18/Sep/17 $$\mathrm{why}\:\mathrm{any}\:\mathrm{infinitely}\:\mathrm{differentiable}\: \\ $$$$\mathrm{function}\:\mathrm{is}\:\mathrm{a}\:\mathrm{power}\:\mathrm{series}? \\ $$$${mathematically}, \\ $$$${if}\:{f}\left({x}\right)\:{is}\:{A}\:{infinitely}\:{differentiable} \\ $$$${function}\:{then}\:{why} \\ $$$${f}\left({x}\right)={ax}^{\mathrm{0}} +{bx}^{\mathrm{1}} +{cx}^{\mathrm{2}} +{dx}^{\mathrm{3}} +{ex}^{\mathrm{4}} +…..…

Question-152310

Question Number 152310 by DELETED last updated on 27/Aug/21 Answered by DELETED last updated on 27/Aug/21 $$\left.\mathrm{1}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}\right)^{\mathrm{10}} \\ $$$$\:\:\:\:\:\:\:\mathrm{simbol}=\mathrm{f}^{'} \left(\mathrm{x}\right)=\frac{\mathrm{dy}}{\mathrm{dx}}=….? \\ $$$$\:\:\:\:\:\:\:\mathrm{misal}:\mathrm{U}=\mathrm{x}^{\mathrm{2}} −\mathrm{x}\rightarrow\frac{\mathrm{dU}}{\mathrm{dx}}=\mathrm{2x}−\mathrm{1} \\…

prove-that-csch-x-1-x-n-1-2-1-n-x-n-2-pi-2-x-2-then-find-0-cosh-x-1-x-x-dx-ln-2-

Question Number 152240 by mnjuly1970 last updated on 26/Aug/21 $$ \\ $$$$\:\:{prove}\:{that}.. \\ $$$$\:\:\:{csch}\:\left({x}\right)=\:\frac{\mathrm{1}}{{x}}\:+\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}.\left(−\mathrm{1}\right)^{\:{n}} \:{x}}{{n}^{\:\mathrm{2}} \pi^{\:\mathrm{2}} +\:{x}^{\:\mathrm{2}} } \\ $$$$\:\:\:{then}\:{find}: \\ $$$$\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\infty}…