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Multiple Choice
Use the graph of f(x)to estimate the value of the limit or state that it does not exist (DNE). limx→−2f(x)
A
−3
B
1
C
4
D
Verified step by step guidance
1
To estimate the limit \( \lim_{x \to -2} f(x) \), we need to observe the behavior of the function \( f(x) \) as \( x \) approaches \( -2 \) from both the left and the right.
Examine the graph to see if the function approaches a specific value as \( x \) approaches \( -2 \). Look for continuity or any jumps, holes, or asymptotes at \( x = -2 \).
From the graph, observe that as \( x \) approaches \( -2 \) from the left, the function appears to be moving towards a certain value. Similarly, check the behavior as \( x \) approaches \( -2 \) from the right.
Notice that the graph shows a jump discontinuity at \( x = -2 \), meaning the left-hand limit and the right-hand limit do not match.
Since the left-hand limit and the right-hand limit are not equal, the limit \( \lim_{x \to -2} f(x) \) does not exist (DNE).