Evaluate the following limits.
$f (x) = {\begin{cases} - x + 6, & x < 0 \\ x + 6, & x \geq 0 \end{cases}$
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$lim_{x \to 0^{-}} f (x) =$
$lim_{x \to 0^{+}} f (x) =$
$lim_{x \to 0} f (x) =$

Answer

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Answer

Since the limits from the left and right are equal, the overall limit exists: $lim_{x \to 0} f (x) = 6$

Steps

Step 1 ：Evaluate the limit from the left: $lim_{x \to 0^{-}} f (x) = - 0 + 6 = 6$

Step 2 ：Evaluate the limit from the right: $lim_{x \to 0^{+}} f (x) = 0 + 6 = 6$

Step 3 ：Since the limits from the left and right are equal, the overall limit exists: $lim_{x \to 0} f (x) = 6$