# How do you find #lim sqrt(x+2)/(sqrt(3x+1)# as #x->oo#?

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To find the limit of sqrt(x+2)/(sqrt(3x+1)) as x approaches infinity, we can use the concept of limits.

First, we divide both the numerator and denominator by sqrt(x) to simplify the expression:

lim (sqrt(x+2)/sqrt(3x+1)) as x->oo = lim (sqrt((x+2)/x)/sqrt((3x+1)/x)) as x->oo = lim (sqrt(1+2/x)/sqrt(3+1/x)) as x->oo

As x approaches infinity, the terms 2/x and 1/x become negligible, so we can simplify further:

lim (sqrt(1+2/x)/sqrt(3+1/x)) as x->oo = sqrt(1/3)

Therefore, the limit of sqrt(x+2)/(sqrt(3x+1)) as x approaches infinity is sqrt(1/3).

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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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