Questions: Given the graph of f(x) above, find the following limits To enter infinity in your answer field, - When you are in text entry mode (when your answer field has just one line), type the word infinity with a lower case i. - When you are in equation editor entry mode (when your answer field has multiple lines with the equation symbol menu bar), choose the symbol infinity to enter infinity. You can switch entry modes by clicking on the button with the upper case Greek letter Sigma next to the answer field. (a) lim x -> 3- f(x)= (b) lim x -> 3+ f(x)=

Given the graph of f(x) above, find the following limits

To enter infinity in your answer field,
- When you are in text entry mode (when your answer field has just one line), type the word infinity with a lower case i.
- When you are in equation editor entry mode (when your answer field has multiple lines with the equation symbol menu bar), choose the symbol infinity to enter infinity.
You can switch entry modes by clicking on the button with the upper case Greek letter Sigma next to the answer field.
(a) lim x -> 3- f(x)=
(b) lim x -> 3+ f(x)=

Transcript text: Given the graph of $f(x)$ above, find the following limits To enter $\infty$ in your answer field, - When you are in text entry mode (when your answer field has just one line), type the word infinity with a lower case i. - When you are in equation editor entry mode (when your answer field has multiple lines with the equation symbol menu bar), choose the symbol $\infty$ to enter $\infty$. You can switch entry modes by clicking on the button with the upper case Greek letter $\Sigma$ next to the answer field. (a) $\lim _{x \rightarrow 3^{-}} f(x)=$ (b) $\lim _{x \rightarrow 3^{+}} f(x)=$

Solution

Solution Steps

To solve the problem of finding the limits of the function $ f(x) $ as $ x $ approaches 3 from the left ($ 3^- $) and from the right ($ 3^+ $), we need to analyze the behavior of the function around $ x = 3 $. This typically involves examining the graph of the function to see how the function values behave as $ x $ gets very close to 3 from both sides. If the graph is not available, we would need the function's expression to determine these limits analytically.

Step 1: Determine the Left-Hand Limit

To find the left-hand limit of the function $ f(x) $ as $ x $ approaches 3, we evaluate: \[ \lim_{x \to 3^{-}} f(x) = 6 \]

Step 2: Determine the Right-Hand Limit

Next, we find the right-hand limit of the function $ f(x) $ as $ x $ approaches 3: \[ \lim_{x \to 3^{+}} f(x) = 6 \]