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Category: Differentiation

Question-44091

Question Number 44091 by peter frank last updated on 21/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18 $$ \\ $$$${ln}\left({y}+\mathrm{1}\right)\left\{\frac{\mathrm{2}\left({y}+\mathrm{1}\right)−{y}}{{y}\left({y}+\mathrm{1}\right)}\right\} \\ $$$${ln}\left({y}+\mathrm{1}\right)\left[\frac{\mathrm{2}}{{y}}−\frac{\mathrm{1}}{{y}+\mathrm{1}}\right] \\ $$$$ \\…

use-the-first-principle-y-ln-cos-x-

Question Number 43854 by peter frank last updated on 16/Sep/18 $${use}\:{the}\:{first}\:{principle}\:{y}=\mathrm{ln}\:\sqrt{\mathrm{cos}\:{x}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 16/Sep/18 $${y}+\bigtriangleup{y}={ln}\sqrt{{cos}\left({x}+\bigtriangleup{x}\right)}\:\: \\ $$$$\bigtriangleup{y}=\frac{\mathrm{1}}{\mathrm{2}}\left\{{ln}\left({cos}\left({x}+\bigtriangleup{x}\right)\right\}−\frac{\mathrm{1}}{\mathrm{2}}\left\{{lncosx}\right\}\right. \\ $$$$\bigtriangleup{y}=\frac{\mathrm{1}}{\mathrm{2}}{ln}\left\{\frac{{cos}\left({x}+\bigtriangleup{x}\right)}{{cosx}}\right\}…

Q-by-using-fourier-series-prove-that-n-1-1-n-1-2n-1-3-3-32-

Question Number 174766 by mnjuly1970 last updated on 10/Aug/22 $$ \\ $$$$\:\:\:\:{Q}:\:\:{by}\:{using}\:{fourier}\:{series}, \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\Omega}=\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\:\boldsymbol{{n}}−\mathrm{1}} }{\left(\mathrm{2}\boldsymbol{{n}}−\mathrm{1}\:\right)^{\:\mathrm{3}} }\:=\:\frac{\boldsymbol{\pi}^{\:\mathrm{3}} }{\mathrm{32}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:−−−−−− \\ $$…