# How do you find the limit of #sqrt(x+e^(4x))/(e^(2x)+x)# as #x->oo#?

Bring the denominator under the square root:

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To find the limit of sqrt(x+e^(4x))/(e^(2x)+x) as x approaches infinity, we can use the concept of limits.

First, we divide both the numerator and denominator by e^(2x). This gives us sqrt((x/e^(2x)) + e^(2x))/(1 + (x/e^(2x))).

As x approaches infinity, the term x/e^(2x) becomes negligible compared to e^(2x). Therefore, we can simplify the expression to sqrt(e^(2x))/1, which is equal to e^x.

Hence, the limit of sqrt(x+e^(4x))/(e^(2x)+x) as x approaches infinity is e^x.

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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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