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Limits are undefined in three scenarios.
1. A vertical asymptote. When the function is a rational function ex. x/x-1. Set the denominator to zero and that is your VA.
2. A hole. When simplifying a function, if two terms cancel out ex. x(x-1)/x-1. Then the term that is canceled out will be your hole when set to zero.
3. A jump discontinuity. This basically when your function jumps to a different y values at certain x value.
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