Category: Differentiation

Question Number 167301 by mnjuly1970 last updated on 12/Mar/22 Answered by amin96 last updated on 12/Mar/22 $$\mathit{I}={\int }_0^{\frac{\pi }{8}}\frac{1}{\sqrt{2}(1-\mathbf{cos}(\frac{\pi }{4}-\mathbf{x}))}\mathbf{dx}\frac{\pi }{4}-\mathbf{x}=\mathbf{t}$$$$$$$$\boldsymbol{\mathrm{t}}\left[\frac{\pi}{\mathrm{8}};\:\frac{\pi}{\mathrm{4}}\right]\:\:\:\:\boldsymbol{{I}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int_{\frac{\pi}{\mathrm{8}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\boldsymbol{\mathrm{dt}}}{\left(\mathrm{1}−\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{t}}\right)\right)}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}}}\int_{\frac{\pi}{\mathrm{8}}}…

Question Number 36178 by prof Abdo imad last updated on 30/May/18 $$letf(x,y)=ln\left(\sqrt{x^2+y^2}\right)$$$$calculate\frac{{\partial }^{2}f}{\partial x^2}(x,y)+\frac{{\partial }^{2}f}{\partial y^2}$$ Commented by abdo…

Question Number 36174 by prof Abdo imad last updated on 30/May/18 $$find{lim}_{(x,y)\to (0,0)}\frac{1-cos\left(\sqrt{xy}\right)}{y}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 36176 by prof Abdo imad last updated on 30/May/18 $$letf(x,y)=(x^2+y^2)sin\left\{\frac{1}{\sqrt{x^2+y^2}}\right\}if(x,y)=(0,0)$$$$andf(0,0)=0$$$$provethatfisdifferenciableatallpointof{R}^2$$$$2)provethat\frac{\partial f}{\partial x}and\frac{\partial f}{\partial y}arenotdifferdnciable$$$${at}\:\left(\mathrm{0},\mathrm{0}\right) \…

Question Number 167230 by mnjuly1970 last updated on 10/Mar/22 $$$$$${lim}_{\alpha \to \mathrm{\infty }}\{\left(\alpha {\int }_0^{\mathrm{\infty }}sin\left(x^{\alpha }\right)dx\right)=\phi \left(\alpha \right)]=\frac{\pi }{2}$$$$----$$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} {sin}\left({x}^{\:\alpha} \right){dx}\:\overset{{x}^{\:\alpha} =\:{y}} {=}\:\frac{\mathrm{1}}{\alpha}\int_{\mathrm{0}}…