Calculus: Other Calculus Problems – #28398

Question: For the function

\[f\left( x \right)=\left\{ \begin{align} & 2\text{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\text{if }x<0 \\ & -{{x}^{2}}+x\,\,\,\,\text{if 0}\le x\le 2 \\ & 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{if }x>2 \\ \end{align} \right.\]

(a) Graph in detail

(b) Find all values of x where the function is discontinuous.

(c) Find the limit from the left and right at any value of x found in part b.

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