# How do you find the limit of # (abs(x+2)-3)/(x-7 ) # as x approaches 7?

and because the numerator is continuous

Note that this gives rise to a singularity and a 2 sided limit.

So we say that:

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The limit does not exist.

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To find the limit of (abs(x+2)-3)/(x-7) as x approaches 7, we can substitute 7 into the expression. However, this results in an undefined expression since the denominator becomes 0. Therefore, we need to simplify the expression before substituting. By factoring the numerator, we get abs(x+2)-3 = abs(x+2)-abs(3), which simplifies to abs(x+2)-abs(3) = abs(x+2)-3. Now, substituting 7 into the simplified expression, we get abs(7+2)-3 = abs(9)-3 = 9-3 = 6. Thus, the limit of (abs(x+2)-3)/(x-7) as x approaches 7 is 6.

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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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