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f-x-sgn-x-2-1-sgn-sin-pix-faind-lim-x-1-f-x-




Question Number 158760 by mathlove last updated on 08/Nov/21
f(x)=[sgn(x^2 −1)+sgn(sin πx)]  faind   lim_(x→1) f(x)=?
$${f}\left({x}\right)=\left[{sgn}\left({x}^{\mathrm{2}} −\mathrm{1}\right)+{sgn}\left(\mathrm{sin}\:\pi{x}\right)\right] \\ $$$${faind}\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=? \\ $$
Commented by mathlove last updated on 08/Nov/21
mister W snswer the Q  andAjfur
$${mister}\:{W}\:{snswer}\:{the}\:{Q} \\ $$$${andAjfur} \\ $$
Commented by mathlove last updated on 08/Nov/21
ajfuor
$${ajfuor} \\ $$
Answered by mr W last updated on 08/Nov/21
f(1)=[0+0]=0  lim_(x→1^− ) f(x)=[−1+1]=0  lim_(x→1^+ ) f(x)=[1−1]=0  ⇒lim_(x→1) f(x)=0
$${f}\left(\mathrm{1}\right)=\left[\mathrm{0}+\mathrm{0}\right]=\mathrm{0} \\ $$$$\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}{f}\left({x}\right)=\left[−\mathrm{1}+\mathrm{1}\right]=\mathrm{0} \\ $$$$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}{f}\left({x}\right)=\left[\mathrm{1}−\mathrm{1}\right]=\mathrm{0} \\ $$$$\Rightarrow\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{0} \\ $$
Commented by mathlove last updated on 09/Nov/21
thanks sir
$${thanks}\:{sir} \\ $$

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