Category: Differentiation

Question Number 63152 by Rio Michael last updated on 29/Jun/19 $$TheVariablesxandysatisfythedifferentialequation$$$$\frac{d^{2}y}{{dx}^2}-x\frac{dy}{dx}+y=x^{2}usetheapproximations$$$$\:\:\:\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)_{{n}} \approx\:\frac{{y}_{{n}+\mathrm{1}} −\mathrm{2}{y}_{{n}} +{y}_{{n}−\mathrm{1}} }{{h}^{\mathrm{2}\:} }\:{and}\:\:\left(\frac{{dy}}{{dx}}\right)\approx\frac{{y}_{{n}+\mathrm{1}}…

Question Number 63015 by ajfour last updated on 27/Jun/19 $$f(x,y,z)=x(p+z)+y(p-z)$$$$+\frac{4x^3}{p+z}+\frac{4y^3}{p-z}+4{(x+y)}^2(y-x)$$$$\mathrm{\forall }p(x,y)=c+(x-y)\sqrt{1+{(x+y)}^2}$$$$+(x^2-y^2)$$$${Determine}\:{x},{y},{z}\:{such}\:{that}\:{f}\:{is} \…

Question Number 128489 by mnjuly1970 last updated on 07/Jan/21 $$\dots calculus\left(2\right)\dots$$$$evaluate::$$$$\underset{n=0}{\sum ^{\mathrm{\infty }}}\left(\frac{2^n}{1+2^{2^n}}\right)=?$$$$$$ Answered by…

Question Number 62809 by mathmax by abdo last updated on 25/Jun/19 $$letf\left(x\right)=arctan\left(nx\right)withnintegrnatural$$$$1)calculate{f}^{\left(n\right)}\left(x\right)and{f}^{\left(n\right)}\left(0\right)$$$$2)developpfatintegrserie.$$ Commented by mathmax by abdo…

Question Number 128225 by mnjuly1970 last updated on 05/Jan/21 $$\dots nicecalculus\dots$$$$provethat:$$$$\varphi ={\int }_0^{\pi }\frac{{tan}^{-1}\left({tan}^2\left(x\right)\right)}{{tan}^2(x}dx\stackrel{???}{=}\pi (\sqrt{2}-\frac{\pi }{4})$$$$$$ Answered…