# How do you find the limit of # (1/(h+2)^2 - 1/4) / h# as h approaches 0?

We need first to manipulate the expression to put it in a more convenient form

Let's work on the expression

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To find the limit of the expression (1/(h+2)^2 - 1/4) / h as h approaches 0, we can simplify the expression first. By combining the fractions and finding a common denominator, we get ((4 - (h+2)^2) / (4(h+2)^2)) / h.

Next, we can simplify further by multiplying the numerator and denominator by h. This gives us (4h - h^3 - 4h - 8) / (4h(h+2)^2).

Simplifying the numerator, we have (-h^3 - 8) / (4h(h+2)^2).

Now, we can factor out a -1 from the numerator, resulting in -(h^3 + 8) / (4h(h+2)^2).

Since we are interested in finding the limit as h approaches 0, we can substitute 0 into the expression. Doing so, we get -(0^3 + 8) / (4(0)(0+2)^2), which simplifies to -8 / 0.

However, division by zero is undefined, so the limit does not exist in this case.

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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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