Question

question 14
let $f(x)=\

$$\begin{cases}8 - x - x^2&\\text{if }x\\leq5\\\\2x - 5&\\text{if }x>5\\end{cases}$$

$
use a graph to determine the following limits. enter dne if the limit doe
$\lim\limits_{x\to5^-}f(x)=$
$\lim\limits_{x\to5^+}f(x)=$
$\lim\limits_{x\to5}f(x)=$

Explanation:

Step1: Left limit at x=5

Use $f(x)=8-x-x^2$
$\lim_{x \to 5^-} f(x) = 8 - 5 - 5^2 = 8 - 5 - 25 = -22$

Step2: Right limit at x=5

Use $f(x)=2x-5$
$\lim_{x \to 5^+} f(x) = 2(5) - 5 = 10 - 5 = 5$

Step3: Overall limit at x=5

Compare left/right limits
Since $\lim_{x \to 5^-} f(x)
eq \lim_{x \to 5^+} f(x)$, the limit does not exist.

Answer:

$\lim_{x \to 5^-} f(x) = -22$
$\lim_{x \to 5^+} f(x) = 5$
$\lim_{x \to 5} f(x) = \text{DNE}$