answer attempt 2 out of 2\n∞ -∞ dne undefined\n$\\lim_{x\\to2^{-}}f(x)=\\square$ $\\lim_{x\\to2^{+}}f(x)=\\sq…

answer attempt 2 out of 2\n∞ -∞ dne undefined\n$\\lim_{x\\to2^{-}}f(x)=\\square$ $\\lim_{x\\to2^{+}}f(x)=\\square$ $\\lim_{x\\to2}f(x)=\\square$ $f(2)=\\square$ submit answer

answer attempt 2 out of 2\n∞ -∞ dne undefined\n$\\lim_{x\\to2^{-}}f(x)=\\square$ $\\lim_{x\\to2^{+}}f(x)=\\square$ $\\lim_{x\\to2}f(x)=\\square$ $f(2)=\\square$ submit answer

Answer

Explanation:

Step1: Analyze left - hand limit

As (x) approaches (2) from the left ((x\to2^{-})), we look at the values of the function (f(x)) as (x) gets closer to (2) from values less than (2). From the graph, the function values are approaching (2). So, (\lim_{x\to2^{-}}f(x) = 2).

Step2: Analyze right - hand limit

As (x) approaches (2) from the right ((x\to2^{+})), we look at the values of the function (f(x)) as (x) gets closer to (2) from values greater than (2). From the graph, the function values are approaching (2). So, (\lim_{x\to2^{+}}f(x)=2).

Step3: Determine the limit

Since (\lim_{x\to2^{-}}f(x)=\lim_{x\to2^{+}}f(x) = 2), then (\lim_{x\to2}f(x)=2).

Step4: Find the function value

The function has a hole at (x = 2), so (f(2)) is undefined.

Answer:

(\lim_{x\to2^{-}}f(x)=2), (\lim_{x\to2^{+}}f(x)=2), (\lim_{x\to2}f(x)=2), (f(2)=\text{undefined})