# What is the limit of #xe^(1/x) - x# as x approaches infinity?

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The limit of xe^(1/x) - x as x approaches infinity 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.

- For what values of x, if any, does #f(x) = 1/((x-5)sin(pi+1/x) # have vertical asymptotes?
- What is # lim_(x->-oo) f(x) = sinx/(x-8)#?
- How do you find the limit of #sqrt(x^2 + 1) - x# as x approaches infinity?
- How do you find the limit of #(2x-3)/(x+5)# as #x->3#?
- How do you find the limit of #sqrt(n^2+n) - (n)# as n approaches #oo#?

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