Exploring Limit Non-Existence in Math: Discontinuity, Oscillation, and More

Limits do not exist when

– the left and right are different (absx/x)- They do not approach the same thing (1/x)- Oscillating behavior (xsin1/x)

there are several cases when limits do not exist. Here are a few common scenarios where limits may not exist:

1. Discontinuity: If a function has a discontinuity at a certain point, then the limit at that point may not exist. This happens when the left-hand and right-hand limits are not equal.

2. Oscillation: If a function oscillates infinitely many times as it approaches a certain point, then the limit at that point does not exist.

3. Infinite limits: If a function approaches infinity or negative infinity as it moves towards a certain point, then the limit does not exist.

4. Undefined functions: If a function is undefined at a certain point, then the limit at that point also does not exist.

5. Indeterminate forms: Certain expressions like 0/0, infinity/infinity, or infinity – infinity produce indeterminate forms, which means that the limit cannot be determined without further analysis.

In general, for a limit to exist, the function must approach the same value from both sides as it gets closer to a certain point.

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