# How do you find the limit of #arctan (x^5-x^-7) # as x approaches infinity?

graph{arctan(x) [-10, 10, -5, 5]}

And if you look at the graph above one more time, you can see that

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To find the limit of arctan(x^5 - x^(-7)) as x approaches infinity, we can use the fact that the arctan function has a range of (-π/2, π/2). As x approaches infinity, the term x^(-7) becomes negligible compared to x^5. Therefore, we can simplify the expression to arctan(x^5).

Since x^5 grows without bound as x approaches infinity, the arctan function will approach its maximum value of π/2. Hence, the limit of arctan(x^5 - x^(-7)) as x approaches infinity is π/2.

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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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