Question

assignment 1
enter each answer as a whole number (like -4, 0, or 253) or dne for undefined or does not exist.
f(4) = 5
lim_{x→6^-} f(x) = 4
lim_{x→4^+} f(x) =
lim_{x→6} f(x) =

Explanation:

Step1: Analyze right - hand limit as x→4

To find $\lim_{x
ightarrow4^{+}}f(x)$, we look at the values of the function as $x$ approaches 4 from the right - hand side. Looking at the graph, as $x$ approaches 4 from the right (values of $x$ slightly greater than 4), the function approaches 1.

Step2: Analyze limit as x→6

To find $\lim_{x
ightarrow6}f(x)$, we need to check if $\lim_{x
ightarrow6^{-}}f(x)=\lim_{x
ightarrow6^{+}}f(x)$. We know $\lim_{x
ightarrow6^{-}}f(x) = 4$. Looking at the graph, as $x$ approaches 6 from the right (values of $x$ slightly greater than 6), the function approaches 3. Since $\lim_{x
ightarrow6^{-}}f(x)
eq\lim_{x
ightarrow6^{+}}f(x)$, $\lim_{x
ightarrow6}f(x)$ does not exist.

Answer:

$\lim_{x
ightarrow4^{+}}f(x)=1$
$\lim_{x
ightarrow6}f(x)=\text{DNE}$