# How do you determine the limit of #-4/(x-5)# as x approaches 5?

left sided limit is

right sided limit is

the nature of the limit requires a little bit more thought

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To determine the limit of -4/(x-5) as x approaches 5, we can substitute the value of 5 into the expression and evaluate it. However, this would result in division by zero, which is undefined. Therefore, we need to use algebraic manipulation to simplify the expression. By factoring the denominator, we can rewrite the expression as -4/[(x-5)(-1)]. Canceling out the common factor of -1, we get 4/(5-x). Now, as x approaches 5, the expression 5-x approaches 0. Therefore, the limit of -4/(x-5) as x approaches 5 is -4/0, which is undefined.

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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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