I’m in AP calc AB, and I’m confused about undefined and DNE, aren’t they both the same? I know the overlap in some instances but there are some problems where it must be either one. I’m confused.
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You understand that a function’s *value* at a point is not necessarily equal to its *limit* at that point, right? For example, `f(x)={1+x if x≠0, 2 if x=0}` has a value of 2 at x=0, but a limit of 1 as x approaches 0.
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Sometimes the limit does not exist even if the value does. For example, `f(x)={|x|/x if x≠0, 0 if x=0}` has a value of 0 at x=0, but doesn’t have a limit as x approaches 0 since it depends which side you approach from.
Sometimes the limit *does* exist even if the value is undefined. For example, `f(x)=(x^2)/x` is undefined at x=0, but its limit as x approaches 0 is 0.
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We wouldn’t normally describe a limit as “undefined”, since the limit of a function is *calculated* based on the definition of that function, not defined directly.
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