# How do you evaluate #[ (ln x) / (csc x) ]# as x approaches 0+?

You can write the function as:

so that:

Both limits are well known, but we can remind how they can be calculated:

We can then conclude that:

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To evaluate [ (ln x) / (csc x) ] as x approaches 0+, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we have [ (1/x) / (-cot x * csc x) ]. Simplifying further, we get [ -cot x / (x * csc x) ]. As x approaches 0+, cot x approaches positive infinity and csc x approaches positive infinity, while x approaches 0. Therefore, the limit of [ -cot x / (x * csc x) ] as x approaches 0+ is negative infinity.

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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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