Question

question 14
let \\( f(x) = \

$$\begin{cases} 10 - x - x^2 & \\text{if } x \\leq 2 \\\\ 2x - 5 & \\text{if } x > 2 \\end{cases}$$

calculate the following limits. enter \dne\ if the limit does
\\( \lim\limits_{x \to 2^-} f(x) = \\)
\\( \lim\limits_{x \to 2^+} f(x) = \\)
\\( \lim\limits_{x \to 2} f(x) = \\)
question help: video

Explanation:

Step1: Left limit, use $x\le2$ formula

Substitute $x=2$ into $10-x-x^2$:
$10 - 2 - 2^2 = 10 - 2 - 4$

Step2: Compute left limit value

$10 - 2 - 4 = 4$

Step3: Right limit, use $x>2$ formula

Substitute $x=2$ into $2x-5$:
$2\times2 - 5$

Step4: Compute right limit value

$4 - 5 = -1$

Step5: Check overall limit existence

Left limit $
eq$ Right limit, so limit DNE.

Answer:

$\lim_{x
ightarrow2^-} f(x) = 4$
$\lim_{x
ightarrow2^+} f(x) = -1$
$\lim_{x
ightarrow2} f(x) = \text{DNE}$