# How do you find the limit of #(ln (e^x - 3*x)) / x# as x approaches infinity?

1

if we scope this out we know that

but clearly we have the indeterminate form here so we can use L'Hopital's Rule

so

it's starting to becomes obvious but we can go one final time with L'Hopital's Rule

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To find the limit of (ln (e^x - 3*x)) / x as x approaches infinity, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (e^x - 3) / (e^x - 3*x). As x approaches infinity, the denominator grows faster than the numerator, so the limit is 1.

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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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