Category: Differentiation

Question Number 144532 by EDWIN88 last updated on 26/Jun/21 $$\mathrm{A}\mathrm{rectangular}\mathrm{box},\mathrm{open}\mathrm{at}\mathrm{the}$$$$\mathrm{top}\mathrm{is}\mathrm{to}\mathrm{have}\mathrm{a}\mathrm{volume}\mathrm{of}32\mathrm{cube}\mathrm{feet}$$$$\mathrm{What}\mathrm{must}\mathrm{be}\mathrm{the}\mathrm{dimensions}$$$$\mathrm{so}\mathrm{that}\mathrm{the}\mathrm{total}\mathrm{surface}\mathrm{is}\mathrm{a}\mathrm{minimum}?$$ Answered by liberty last updated on 26/Jun/21…

Question Number 144525 by imjagoll last updated on 26/Jun/21 $$\mathrm{If}\mathrm{y}=\cosh ({\mathrm{x}}^2-3\mathrm{x}+1)$$$$\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}=?$$ Answered by EDWIN88 last updated on 26/Jun/21 $$\:\mathrm{let}\:\mathrm{q}\:=\:\mathrm{x}^{\mathrm{2}}…

Question Number 13429 by sergiosba last updated on 20/May/17 Commented by prakash jain last updated on 20/May/17 $$x=-2\cos \theta$$$$y=3\sin \theta$$$$\cos \theta =-\frac{x}{2}$$$$\mathrm{sin}\:\theta=\frac{{y}}{\mathrm{3}} \…

Question Number 144389 by liberty last updated on 25/Jun/21 $$\int (\mathrm{x}-1)\mathrm{h}\left(\mathrm{x}\right)\mathrm{dx}={\mathrm{x}}^3-\sin 2\mathrm{x}+\sqrt{{\mathrm{x}}^2+1}+\mathrm{c}$$$$\Rightarrow \mathrm{h}{}^{\prime }\left(1\right)=?$$ Answered by mathmax by abdo last updated on 25/Jun/21…

Question Number 144311 by mnjuly1970 last updated on 24/Jun/21 $$$$$$\dots \dots \mathrm{Nice}\dots .\mathrm{Calculus}\dots \dots$$$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}::$$$$$$$$\mathrm{\Theta }:=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{4^n{cos}^2\left(\frac{\pi }{2^{n+2}}\right)}=?$$$$\:\:\:\:……….…