# #lim_(x -> 0) 1/x (2/(2+x)^3-1/4) = # ?

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Distribute the

Make a common denominator

Simplify

Evaluate at 0

We are aware that there are clever ways to multiply each fraction by one to create a common denominator:

Execute the multiplication:

Over the common denominator, add the numerators:

In the numerator, enlarge the cube:

Assign the -1:

Removing a common factor of x is possible:

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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.

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