Category: Differentiation

Question Number 56069 by necx1 last updated on 09/Mar/19 $$Findtheexpansionandtheconvergemce$$$$ofthefollowinginthepowerofx:$$$$\left(i\right)sinx$$$$\left(ii\right)\ln (1+x)$$$$\left(iii\right){\tan }^{-1}x$$ Commented by tanmay.chaudhury50@gmail.com last…

Question Number 121400 by rs4089 last updated on 07/Nov/20 $$indmaximumvalueof\sqrt{x^4+y^4}$$ Answered by MJS_new last updated on 07/Nov/20 $$\mathrm{for}\:{x},\:{y}\:\in\mathbb{R}:\:\mathrm{0}\leqslant\sqrt{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }<+\infty \…

Question Number 121361 by rs4089 last updated on 07/Nov/20 Answered by TANMAY PANACEA last updated on 07/Nov/20 $$u=x^3{sin}^{-1}\left(\frac{y}{x}\right)-y^3{sin}^{-1}\left(\frac{x}{y}\right)$$$$={x}^{\mathrm{3}} \left\{{sin}^{−\mathrm{1}}…

Question Number 121353 by john santu last updated on 06/Nov/20 Answered by liberty last updated on 07/Nov/20 $$\mathrm{Let}\mathrm{x}\mathrm{be}\mathrm{the}\mathrm{x}-\mathrm{coordinate}\mathrm{of}\mathrm{end}\mathrm{point}$$$$\mathrm{that}\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{x}-\mathrm{axis}\mathrm{and}\mathrm{let}\mathrm{the}\mathrm{other}$$$$\mathrm{endpoint}\mathrm{be}(0,\mathrm{y}).\mathrm{Thus}\mathrm{there}\mathrm{is}\mathrm{a}\mathrm{function}$$$$\mathrm{f}\:\mathrm{which}\:\mathrm{gives}\:\mathrm{y}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}.\:\mathrm{Since} \…

Question Number 121264 by benjo_mathlover last updated on 06/Nov/20 $$\mathrm{Find}\mathrm{the}\mathrm{point}\mathrm{on}\mathrm{the}\mathrm{curve}$$$$\mathrm{x}={2\mathrm{y}}^2\mathrm{closest}\mathrm{to}\mathrm{the}\mathrm{point}$$$$(10,0)$$ Answered by liberty last updated on 06/Nov/20 $$\mathrm{Let}\:\mathrm{L}\:\mathrm{be}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{distance}\:\mathrm{between}…