Menu Close

g-x-x-2-1-ln-x-Study-the-variations-of-the-function-g-and-draw-up-its-table-of-variations-




Question Number 171284 by Kodjo last updated on 11/Jun/22
g(x)=−x^2 +1−ln∣x∣  Study the variations of the function g and draw up its table of variations
$${g}\left({x}\right)=−{x}^{\mathrm{2}} +\mathrm{1}−{ln}\mid{x}\mid \\ $$Study the variations of the function g and draw up its table of variations

Answered by a.lgnaoui last updated on 12/Jun/22
Answered by a.lgnaoui last updated on 12/Jun/22
pour x<0   g(x)=x^2 +1−ln(−x)  g′(x)=2x+(1/x)=((2x^2 +1)/x)<0 g(x) decroissant  x     −∞                               0          +∞               \          −∞  limg(x)_(x→−∞) =2x−(1/(−x))=2x+(1/x)=+∞  limg(x)_(x→−0) =−∞
$${pour}\:{x}<\mathrm{0}\:\:\:{g}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{1}−{ln}\left(−{x}\right) \\ $$$${g}'\left({x}\right)=\mathrm{2}{x}+\frac{\mathrm{1}}{{x}}=\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}}{{x}}<\mathrm{0}\:{g}\left({x}\right)\:{decroissant} \\ $$$${x}\:\:\:\:\:−\infty\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:+\infty\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\backslash\:\:\:\:\:\:\:\:\:\:−\infty \\ $$$${limg}\left({x}\right)_{{x}\rightarrow−\infty} =\mathrm{2}{x}−\frac{\mathrm{1}}{−{x}}=\mathrm{2}{x}+\frac{\mathrm{1}}{{x}}=+\infty \\ $$$${limg}\left({x}\right)_{{x}\rightarrow−\mathrm{0}} =−\infty \\ $$$$ \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *