For the piecewise linear function, find the following. (If an \[ f(x)=\left\{\begin{array}{ll} 4-x & \text { if } x \leq 5 \\ 13-2 x & \text { if } x>5 \end{array}\right. \] (a) $\lim _{x \rightarrow 5^{-}} f(x)$ (b) $\lim _{x \rightarrow 5^{+}} f(x)$ (c) $\lim _{x \rightarrow 5} f(x)$

Step 1 ：The problem is asking for the limit of the function f(x) as x approaches 5 from the left, from the right, and in general. The limit of a function as x approaches a certain value is the value that the function approaches as x gets closer and closer to that value.

Step 2 ：For a piecewise function like this one, we can calculate the limit by plugging in the value of x into the appropriate piece of the function.

Step 3 ：For (a), since we're approaching 5 from the left (i.e., x is less than 5), we should use the first piece of the function, 4 - x.

Step 4 ：For (b), since we're approaching 5 from the right (i.e., x is greater than 5), we should use the second piece of the function, 13 - 2x.

Step 5 ：For (c), if the two one-sided limits from (a) and (b) are equal, then that is the general limit as x approaches 5. If they are not equal, then the limit as x approaches 5 does not exist.

Step 6 ：The limit as x approaches 5 from the left is -1, and the limit as x approaches 5 from the right is 3. Since these two limits are not equal, the general limit as x approaches 5 does not exist.

Step 7 ：Final Answer: (a) \(\lim _{x \rightarrow 5^{-}} f(x) = \boxed{-1}\)

Step 8 ：Final Answer: (b) \(\lim _{x \rightarrow 5^{+}} f(x) = \boxed{3}\)

Step 9 ：Final Answer: (c) \(\lim _{x \rightarrow 5} f(x)\) does not exist.