# How do you evaluate # [ ( ln x ) / (x^2 + x - 2 )]# as x approaches 1?

To find the limit using L'Hopitals rule simple evaluate the same limit for the derivative of the numerator over the derivative of the denominator.

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To evaluate the expression [(ln x) / (x^2 + x - 2)] as x approaches 1, we substitute 1 into the expression. This gives us [(ln 1) / (1^2 + 1 - 2)]. Since ln 1 is equal to 0, the expression simplifies to 0 / 0. This is an indeterminate form, so we need to apply L'Hôpital's rule. By taking the derivative of the numerator and denominator separately, we get [(1/x) / (2x + 1)]. Substituting x = 1 into this new expression gives us [(1/1) / (2(1) + 1)], which simplifies to 1/3. Therefore, as x approaches 1, the expression [(ln x) / (x^2 + x - 2)] evaluates to 1/3.

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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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