# What is the limit of #(x - ln x)# as x approaches #oo#?

This limit goes unbounded to

are differentiable everywhere, we can use L'Hospital's rule:

Therefore,

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The limit of (x - ln x) as x approaches infinity is infinity.

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The limit of ( (x - \ln(x)) ) as ( x ) approaches infinity (denoted as ( \infty )) is ( \infty ).

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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.

- What is # lim_(->-oo) f(x) = e^-x#?
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- How do you evaluate the limit #sqrt(x^2-2)-sqrt(x^2+1)# as x approaches #oo#?
- How do you find the limit of #(x^2+x-12)/(x-2)# as #x->2#?
- How do you find the limit of # ((1/y) - (1/7))/(y-7)# as y approaches 7?

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