# What is #\lim_{x \rightarrow 0+} \tan^{- 1} ( \ln x )#?

We can proceed by steps, noting first that:

so:

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The limit of arctan(ln(x)) as x approaches 0 from the right is equal to -pi/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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