Menu Close

Category: Differentiation

Question-115750

Question Number 115750 by shahria14 last updated on 28/Sep/20 Answered by Dwaipayan Shikari last updated on 28/Sep/20 $$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{log}\left(\mathrm{1}+\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \right)}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }=\mathrm{1} \\ $$$$\mathrm{log}\left(\mathrm{1}+\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \right)=\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{approx}\right)…

Given-xy-1-3-for-x-y-R-find-min-value-of-4-x-6-9-y-6-

Question Number 115733 by bemath last updated on 28/Sep/20 $${Given}\:{xy}\:=\frac{\mathrm{1}}{\mathrm{3}}\:{for}\:{x},{y}\in\mathbb{R}\: \\ $$$${find}\:{min}\:{value}\:{of}\:\frac{\mathrm{4}}{{x}^{\mathrm{6}} }+\frac{\mathrm{9}}{{y}^{\mathrm{6}} } \\ $$ Answered by MJS_new last updated on 28/Sep/20 $${y}=\frac{\mathrm{1}}{\mathrm{3}{x}}\:\Rightarrow\:\frac{\mathrm{4}}{{x}^{\mathrm{6}} }+\frac{\mathrm{9}}{{y}^{\mathrm{6}}…

Find-the-supremum-and-the-infimum-of-x-sin-x-on-the-interval-0-pi-2-

Question Number 115516 by bobhans last updated on 26/Sep/20 $${Find}\:{the}\:{supremum}\:{and}\:{the}\:{infimum} \\ $$$${of}\:\frac{{x}}{\mathrm{sin}\:{x}}\:{on}\:{the}\:{interval}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\:\right] \\ $$ Commented by john santu last updated on 26/Sep/20 $${infimum}\:{y}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mathrm{sin}\:{x}}\:=\:\mathrm{1} \\…