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

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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Some examples in which the limit does not exist include:

- When the function approaches different values from the left and right sides of a specific point.
- When the function oscillates or fluctuates infinitely as it approaches a certain point.
- When the function approaches positive or negative infinity as it approaches a specific point.
- When the function has a jump discontinuity at a certain point.
- When the function has an essential discontinuity at a certain point.
- When the function has a removable discontinuity at a certain point.

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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.

- How do you find the limit of # (sin^2(x^2))/(x^4)# as x approaches 0?
- How do you find the limit of #(sqrt(6-x)-2)/(sqrt(3-x) -1)# as x approaches 2?
- Evaluate #lim_(x rarr -oo) sqrt(x^2 + x) - x #?
- How do you find #lim sqrt(u^2-3u+2)-sqrt(u^2+1)# as #u->oo#?
- How do you evaluate # (3x^2 - x) /( 7x^2 - 10)# as x approaches infinity?

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