Limits and Direct Substitution

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Direct substitution can be misleading when evaluating limits, as it requires both left and right hand limits to be equal for the limit to exist. The discussion highlights that while answer choices A and B were identified, answer choice C may not hold true if f(0) is undefined or does not equal 2. The possibility of a removable discontinuity at x=2 is emphasized, indicating that the function's behavior at that point is crucial for determining the limit. Therefore, careful analysis is necessary to ascertain the validity of all answer choices. Understanding these concepts is essential for accurately solving limit problems.
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Why wouldn't answer choice "C" be true as well?

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Homework Equations



I thought that you could use direct substitution on this limit.

The Attempt at a Solution



I did get answer choices A and B. For the limit to exist, both the left and right hand limits have to match up.
 
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f(0) might not be defined or it may be that f(0)≠2. In other words, f(x) might have a removable discontinuity at x=2.
 

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