Don't Overthink It!

Calculus Level 2

What is the value of \[\lim_{x \to 4} f(x)\]

If \[f(x) = \begin{cases} |x+3-x^2| & \text{if } -\infty \leq x < 2 , \text{and }5<x \leq \infty\\\frac {1}{2} \times |x| +2 & \text{if } 2 \leq x \leq 5 \text{ for } x \neq 4\\20 & \text{if } x=4. \end{cases} \]

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