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Question Number 85871 by M±th+et£s last updated on 25/Mar/20

Commented by Rio Michael last updated on 25/Mar/20

$$\mathrm{all}\mathrm{integers}$$

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

$$allintegersexcept1.$$$$x=1+\delta$$$$f\left(x\right)={[1+d]}^2-\left[{(1+d)}^2\right]$$$$\underset{x\to 1^{+}}{\lim }f\left(x\right)=\underset{\delta \to 0}{\lim }\{{[1+d]}^2-\left[{(1+d)}^2\right]\}=1-1=0$$$$x=1-\delta$$$$f\left(x\right)={[1-d]}^2-\left[{(1-d)}^2\right]$$$$\underset{x\to 1^{-}}{\lim }f\left(x\right)=\underset{\delta \to 0}{\lim }\{{[1-d]}^2-\left[{(1-d)}^2\right]\}=0-0=0$$$$f\left(1\right)=1-1=0$$$$$$$$\underset{x\to 1^{-}}{\lim }f\left(x\right)=\underset{x\to 1^{+}}{\lim }f\left(x\right)=f\left(1\right)$$$$\Rightarrow continuousatx=1$$

Commented by M±th+et£s last updated on 25/Mar/20

$$thankyousomuchsir$$

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