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Category: Differentiation

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}…

help-given-total-cost-4x-y-p-1-25-3x-2y-p-2-12-x-y-total-revenue-p-1-x-p-2-y-calculate-a-quantity-sold-for-each-item-to-get-maximum-profit-b-respective-price-for-each-item-c-the-ma

Question Number 86537 by zainal tanjung last updated on 29/Mar/20 $$\mathrm{help}\: \\ $$$$\mathrm{given}\:\mathrm{total}\:\mathrm{cost}=\mathrm{4x}+\mathrm{y} \\ $$$$\mathrm{p}_{\mathrm{1}} =\mathrm{25}−\mathrm{3x}−\mathrm{2y} \\ $$$$\mathrm{p}_{\mathrm{2}} =\mathrm{12}−\mathrm{x}−\mathrm{y} \\ $$$$\mathrm{total}\:\mathrm{revenue}=\mathrm{p}_{\mathrm{1}} \mathrm{x}+\mathrm{p}_{\mathrm{2}} \mathrm{y} \\ $$$$\mathrm{calculate}:…

Question-20903

Question Number 20903 by ANTARES_VY last updated on 07/Sep/17 Answered by Joel577 last updated on 07/Sep/17 $$\mathrm{Using}\:\mathrm{polynomial}\:\mathrm{division},\mathrm{we}\:\mathrm{got} \\ $$$${I}\:=\:\int\:{x}^{\mathrm{3}} \:−\:{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:−\:\mathrm{4}\:+\:\frac{\mathrm{4}{x}\:+\:\mathrm{1}}{{x}^{\mathrm{2}} \:+\:{x}}\:{dx} \\ $$$$\:\:\:=\:\int\:{x}^{\mathrm{3}} \:−\:{x}^{\mathrm{2}}…