What are some examples in which the limit does not exist?

Answer 1

One example is when the right and left limits are different. So in that particular point the limit doesn't exist.
For example: if you compress a gas the volume abruptly changes (in changing phase):

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Answer 2

Some examples in which the limit does not exist include:

  1. When the function approaches different values from the left and right sides of a specific point.
  2. When the function oscillates or fluctuates infinitely as it approaches a certain point.
  3. When the function approaches positive or negative infinity as it approaches a specific point.
  4. When the function has a jump discontinuity at a certain point.
  5. When the function has an essential discontinuity at a certain point.
  6. When the function has a removable discontinuity at a certain point.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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