# What is the root of #x^3 - x - 1 = 0# in exact form?

Real root:

#root(3)((27+3sqrt(69))/54)+root(3)((27-3sqrt(69))/54)#

and related complex roots...

Given:

Then:

So:

and our equation can be rewritten:

Hence by the quadratic formula:

and related complex roots:

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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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