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Question Number 54688 by pooja24 last updated on 09/Feb/19

$$f\left(x\right)=\frac{2\left[x\right]}{3x-\left[x\right]}examineitscontinuityatx=\frac{-1}{2}$$$$where\left[x\right]isgreatestintegerfunction$$

Commented by maxmathsup by imad last updated on 10/Feb/19

$$wehavef(-\frac{1}{2})=\frac{2(-1)}{-\frac{3}{2}-(-1)}=\frac{-2}{-\frac{3}{2}+1}=\frac{-2}{-\frac{1}{2}}=4$$$$and{lim}_{x\to {(-\frac{1}{2})}^{+}}f\left(x\right)={lim}_{x\to {(-\frac{1}{2})}^{-}}f\left(x\right)=4=f(-\frac{1}{2})sofiscontinueat$$$$x_0=-\frac{1}{2}.$$

Answered by kaivan.ahmadi last updated on 09/Feb/19

$$\mathrm{f}(-\frac{1}{2})=\mathrm{li}\underset{\mathrm{x}\to -\frac{1^{+}}{2}}{\mathrm{m}f}\left(\mathrm{x}\right)=\mathrm{li}\underset{\mathrm{x}\to -\frac{1^{-}}{2}}{\mathrm{m}f}\left(\mathrm{x}\right)=4$$$$\mathrm{so}\mathrm{f}\mathrm{is}\mathrm{continuos}\mathrm{at}\mathrm{x}=-\frac{1}{2}$$

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