# How do you evaluate the limit #((3+h)^3-27)/h# as h approaches #0#?

Then:

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To evaluate the limit ((3+h)^3-27)/h as h approaches 0, we can simplify the expression by expanding (3+h)^3 using the binomial theorem. This gives us (27 + 27h + 9h^2 + h^3 - 27)/h. Simplifying further, we get (27h + 9h^2 + h^3)/h. Canceling out the h in the numerator and denominator, we are left with 27 + 9h + h^2. Now, as h approaches 0, the limit of this expression is 27.

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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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