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lim-x-3-x-3-x-3-show-right-and-left-side-limit-




Question Number 126427 by Study last updated on 20/Dec/20
lim_(x→−3) ((∣x+3∣)/(x+3))      show right and left side  limit??
$${li}\underset{{x}\rightarrow−\mathrm{3}} {{m}}\frac{\mid{x}+\mathrm{3}\mid}{{x}+\mathrm{3}}\:\:\:\:\:\:{show}\:{right}\:{and}\:{left}\:{side} \\ $$$${limit}?? \\ $$
Answered by liberty last updated on 20/Dec/20
lim_(x→−3^− ) [ ((∣x+3∣)/(x+3)) ] = lim_(x→−3^− )  ((−(x+3))/(x+3)) = −1  lim_(x→−3^+  )  [ ((∣x+3∣)/(x+3)) ] = lim_(x→−3^+ )  ((x+3)/(x+3)) = 1
$$\underset{{x}\rightarrow−\mathrm{3}^{−} } {\mathrm{lim}}\left[\:\frac{\mid{x}+\mathrm{3}\mid}{{x}+\mathrm{3}}\:\right]\:=\:\underset{{x}\rightarrow−\mathrm{3}^{−} } {\mathrm{lim}}\:\frac{−\left({x}+\mathrm{3}\right)}{{x}+\mathrm{3}}\:=\:−\mathrm{1} \\ $$$$\underset{{x}\rightarrow−\mathrm{3}^{+} \:} {\mathrm{lim}}\:\left[\:\frac{\mid{x}+\mathrm{3}\mid}{{x}+\mathrm{3}}\:\right]\:=\:\underset{{x}\rightarrow−\mathrm{3}^{+} } {\mathrm{lim}}\:\frac{{x}+\mathrm{3}}{{x}+\mathrm{3}}\:=\:\mathrm{1} \\ $$$$ \\ $$
Commented by liberty last updated on 20/Dec/20
Commented by Study last updated on 21/Dec/20
i don′t know
$${i}\:{don}'{t}\:{know} \\ $$
Commented by liberty last updated on 22/Dec/20
good !
$${good}\:! \\ $$

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