# How do you evaluate the limit #(x-1)/(x^2-1)# as x approaches #1#?

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To evaluate the limit (x-1)/(x^2-1) as x approaches 1, we can substitute the value of x into the expression. However, this would result in division by zero, which is undefined. Therefore, we need to simplify the expression before substituting the value of x. Factoring the denominator, we get (x-1)(x+1). Canceling out the common factor of (x-1), we are left with 1/(x+1). Now, we can substitute x=1 into this simplified expression, which gives us 1/(1+1) = 1/2. Therefore, the limit of (x-1)/(x^2-1) as x approaches 1 is equal to 1/2.

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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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