Category: Differentiation

Question Number 132905 by bramlexs22 last updated on 17/Feb/21 Answered by bobhans last updated on 17/Feb/21 $$Totalsurfacearea=A=\pi rh+2hr+\pi r^2=200{cm}^2$$$$h=\frac{200-\pi r^2}{2r+\pi r}$$$${Vol}\:{of}\:{block}\:=\:{V}=\:\frac{\mathrm{1}}{\mathrm{2}}\pi{r}^{\mathrm{2}} {h} \…

Question Number 132753 by liberty last updated on 16/Feb/21 $$\mathrm{Given}\mathrm{x},\mathrm{y}\in \mathbb{R},\mathrm{x},\mathrm{y}\ne 0$$$$\mathrm{Find}\mathrm{the}\mathrm{maximum}\mathrm{and}\mathrm{minimum}$$$$\mathrm{value}\mathrm{of}\frac{\mathrm{xy}-{4\mathrm{y}}^2}{{\mathrm{x}}^2+{4\mathrm{y}}^2}$$ Commented by mr W last updated…

Question Number 1676 by hhhggvghhh last updated on 31/Aug/15 $$\mathit{h}\mathit{h}\mathit{j}\mathit{g}\mathit{h}\mathit{h}\mathit{j}\mathit{j}\mathit{g}\mathit{k}\mathit{g}\mathit{g}\mathit{j}\mathit{g}\mathit{g}\mathit{i}\mathit{g}\mathit{f}\mathit{h}\mathit{p}\mathit{p}\mathit{p}\mathit{k}\mathit{k}\mathit{n}\mathit{b}\mathit{g}\mathit{j}\mathit{f}\mathit{f}\mathit{f}\mathit{f}\mathit{g}$$$$\mathit{b}\mathit{i}\mathit{u}\mathit{g}\mathit{g}\mathit{j}\mathit{n}\mathit{g}\mathit{g}\mathit{t}\mathit{b}\mathit{n}\mathit{k}\mathit{o}\mathit{y}\mathit{f}\mathit{h}\mathit{j}\mathit{i}\mathit{u}\mathit{h}\mathit{b}\mathit{h}\mathit{u}\mathit{k}\mathit{l}\mathit{p}\mathit{h}\mathit{h}$$$$\mathit{j}\mathit{i}\mathit{n}\mathit{b}\mathit{h}678656\mathit{k}\mathit{k}\mathit{i}\mathit{o}\mathit{h}\mathit{h}\mathit{u}\mathit{g}\mathit{g}\mathit{j}\mathit{n}\mathit{g}\mathit{f}\mathit{f}\mathit{j}\mathit{k}\mathit{k}\mathit{d}\mathit{o}\mathit{o}\mathit{x}\mathit{k}$$$$\mathit{i}\mathit{k}\mathit{h}\mathit{h}\mathit{k}\mathit{j}\mathit{h}\mathit{v}2[65\sqrt{\sqrt{58889<\mathit{l}\mathit{k}\mathit{k}\mathit{j}\mathit{k}\mathit{b}\mathit{m}\mathit{b}\mathit{b}\mathit{n}\mathit{n}\mathit{b}}}$$$$\mathit{j}\mathit{k}\mathit{k}\mathit{h}\mathit{j}\mathit{m}\sqrt{\mathit{n}\mathit{l}\mathit{m}6\mathit{j}\mathit{i}\mathit{k}\mathit{m}\mathit{b}\mathit{h}\sqrt{\mathit{j}\mathit{l}\mathit{b}\mathit{j}}}$$$$\mathit{j}\mathit{l}\mathit{j}\mathit{b}\mathit{n}\mathit{k}\mathit{b}\mathit{b}\mathit{n}\mathit{m}\mathit{n}\mathit{m}\mathit{m}\mathit{n}\mathit{j}\mathit{k}\mathit{n}\mathit{b}\mathit{j}\mathit{n}\mathit{r}\mathit{u}\mathit{r}\mathit{u}\mathit{b}\mathit{v}\underset{\mathit{n}\mathit{k}\mathit{j}\mathit{n}\mathit{b}\mathit{m}\mathit{m}}{\mathit{m}}$$$${\mathit{j}\mathit{j}\mathit{n}\mathit{b}\mathit{b}\mathit{n}\mathit{j}\mathit{n}\mathit{n}\mathit{j}}^{}$$$$\boldsymbol{{nkn}}…

Question Number 1624 by 112358 last updated on 27/Aug/15 $$Findthefirstderivativeof$$$$y\left(x\right)=\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+\dots }}}}}$$$$fromfirstprinciples.$$$$$$ Commented by Rasheed Soomro last updated on…

Question Number 132477 by KZ last updated on 14/Feb/21 $$define$$$$f(x.y)=$$$$\{\frac{\mathrm{xy}({\mathrm{x}}^2-{\mathrm{y}}^2)}{x^2+y^2}if(x.y)\ne )0.0)$$$$0if(x.y)=(0.0)$$$$$$$${show}\:{that}\:{f},\frac{\partial{f}}{\partial{x}}\:{and}\:\frac{\partial{f}}{\partial{y}\:\:}\:{are}\: \…