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Locate the point of discontinuity of the function   \(f(x) = \begin{cases} (x^3-x^2+ 2x -2) , & \quad \text{if } x≠1; \text{}\\ 4, & \quad \text{if } x=0\text{} \end{cases}\) 

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Given function  \(f(x) = \begin{cases} (x^3-x^2+ 2x -2) , & \quad \text{if } x≠1; \text{}\\ 4, & \quad \text{if } x=1\text{} \end{cases}\) 

= 1 – 1 + 2 – 2 

= 0

Also, f(1) = 4 

As we can see that, 

\(\lim\limits_{x \to 1^-}\) f(x) = \(\lim\limits_{x \to 1^+}\) f(x)≠f(1)

Therefore, 

f(x) is not continuous at x = 1

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