# How do you find the limit #lim (root4(x+1)-root4x)x^(3/4)# as #x->oo#?

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To find the limit of the expression lim (root4(x+1)-root4x)x^(3/4) as x approaches infinity, we can simplify the expression first.

Using the property of radicals, we can simplify root4(x+1) - root4x as (x+1)^(1/4) - x^(1/4).

Next, we multiply this simplified expression by x^(3/4).

Now, we have the expression (x+1)^(1/4) - x^(1/4) multiplied by x^(3/4).

To evaluate the limit as x approaches infinity, we can use the fact that the dominant term in the expression will determine the limit.

Since x^(3/4) grows faster than (x+1)^(1/4) and x^(1/4), the dominant term is x^(3/4).

Therefore, as x approaches infinity, the limit of the expression is infinity.

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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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