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Question Number 82897 by aseer imad last updated on 25/Feb/20

Commented by mr W last updated on 25/Feb/20

$$certainly!$$$$\underset{x\to 0}{\lim }f\left(x\right)=f\left(0\right)=0+1+2=3$$$$\underset{x\to 1}{\lim }f\left(x\right)=f\left(1\right)=1+0+1=2$$$$\underset{x\to 2}{\lim }f\left(x\right)=f\left(2\right)=2+1+0=3$$

Commented by aseer imad last updated on 25/Feb/20

thank you

Answered by TANMAY PANACEA last updated on 25/Feb/20

$$criticalvalueofx=0,1,2$$$$f\left(x\right)=x+x-1+x-2whenx>2$$$$=3x-3$$$$=x+x-1-(x-2)when2>x>1$$$$=x+1$$$$=x-(x-1)-(x-2)when1>x>0$$$$=-x+3$$$$=-\left(x\right)-(x-1)-(x-2)whenx<0$$$$=-3x+3$$$$\mathit{n}\mathit{o}\mathit{w}$$$$\underset{x\to 0+}{\lim }\mathit{f}\left(\mathit{x}\right)$$$$\underset{x\to 0+}{\lim }-\mathit{x}+3=3$$$$\underset{x\to 0-}{\lim }\mathit{f}\left(\mathit{x}\right)$$$$=\underset{x\to 0-}{\lim }-3\mathit{x}+3=3$$$$\mathit{s}\mathit{o}\mathit{l}\mathit{i}\mathit{m}\mathit{i}\mathit{t}\mathit{e}\mathit{x}\mathit{i}\mathit{s}\mathit{t}\mathit{a}\mathit{t}\mathit{x}=0$$$$\underset{x\to 1+}{\lim }\mathit{f}\left(\mathit{x}\right)$$$$\underset{x\to 1+}{\lim }\mathit{x}+1=2$$$$\underset{x\to 1-}{\lim }-\mathit{x}+3=-1+3=2$$$$\mathit{l}\mathit{i}\mathit{m}\mathit{i}\mathit{t}\mathit{e}\mathit{x}\mathit{i}\mathit{s}\mathit{t}\mathit{a}\mathit{t}\mathit{x}=1$$$$\underset{x\to 2-}{\lim }\mathit{x}+1=3$$$$\underset{x\to 2+}{\lim }3\mathit{x}-3=3$$$$solimitexistatx=1,2and3$$$$plscheck...$$$$$$$$$$$$$$

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