Question - Piecewise Graph Limit Calculation
Solution:
The image presents a piecewise graph of the function y = f(x) and asks for the value of the expression:\[ \lim_{x \to -4^+} f(x) - \lim_{x \to 0^-} f(x) + \lim_{x \to 2^+} f(x) \]From the graph, we can derive the following limits:1. $$ \lim_{x \to -4^+} f(x) $$ is the value that f(x) approaches as x approaches -4 from the right. By looking at the graph, we can see this value is n.2. $$ \lim_{x \to 0^-} f(x) $$ is the value that f(x) approaches as x approaches 0 from the left. On the graph, this value is m.3. $$ \lim_{x \to 2^+} f(x) $$ is the value that f(x) approaches as x approaches 2 from the right. The graph shows this value as k.Now, we substitute these values into the given expression:n (the limit as x approaches -4 from the right) - m (the limit as x approaches 0 from the left) + k (the limit as x approaches 2 from the right).From the graph, we can infer the following based on the labelled points:- n is at y = -1- m is at y = 1- k is at y = 0Using these values:$$ \lim_{x \to -4^+} f(x) = -1 $$$$ \lim_{x \to 0^-} f(x) = 1 $$$$ \lim_{x \to 2^+} f(x) = 0 $$Substitute these values into the expression:\[ (-1) - (1) + (0) = -2 \]Therefore, the value of the given expression is -2.
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