# How do you find the limit #(5+x^-1)/(1+2x^-1)# as #x->oo#?

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To find the limit of (5+x^-1)/(1+2x^-1) as x approaches infinity, we can use the concept of limits.

First, we simplify the expression by multiplying both the numerator and denominator by x to get (5x + 1)/(x + 2x^2).

Next, as x approaches infinity, the terms with lower powers of x become negligible compared to the highest power term. Therefore, we can ignore the 1 in the numerator and the x in the denominator.

This simplifies the expression to 5x/x^2, which further simplifies to 5/x.

Finally, as x approaches infinity, the value of 5/x approaches 0.

Therefore, the limit of (5+x^-1)/(1+2x^-1) as x approaches infinity is 0.

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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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