Q:

Please help with these 2 questions. Will give brainliest to best asnwer

Accepted Solution

A:
First Image:
[tex] \lim_{x \to 2^{-} }[/tex]f(x) means limit of f(x) as x approaches to 2 from negative side i.e. the left side. As seen from the graph, as we approach 2 from left hand side, the graph of f(x) approaches 3.
So, [tex] \lim_{x \to 2^{-} }[/tex]f(x) = 3

[tex] \lim_{x \to 2^{+} }[/tex] means limit of f(x) as x approaches to 2 from positive side i.e. the right side. As seen from the graph, as we approach 2 from right hand side, the graph of f(x) approaches -3.
So, [tex] \lim_{x \to 2^{+} }[/tex]f(x) = -3

Second Image:
[tex] \lim_{x \to 3^{-} }[/tex]f(x) means limit of f(x) as x approaches to 3 from negative side i.e. the left side. As seen from the graph, as we approach 3 from left hand side, the graph of f(x) approaches -1.
So, [tex] \lim_{x \to 3^{-} }[/tex]f(x) = -1