# How do you evaluate the limit #(x^4-10)/(4x^3+x)# as x approaches #oo#?

So:

You can see that by separating the sum:

Evidently:

graph{(x^4-10)/(4x^3+x) [-10, 10, -5, 5]}

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To evaluate the limit of (x^4-10)/(4x^3+x) as x approaches infinity, we can use the concept of dominant terms. By dividing both the numerator and denominator by x^3, we get (x^4/x^3 - 10/x^3)/(4x^3/x^3 + x/x^3). Simplifying this expression, we have (x - 10/x^3)/(4 + 1/x^2). As x approaches infinity, the term 10/x^3 becomes negligible compared to x, and 1/x^2 becomes negligible compared to 4. Therefore, the limit simplifies to x/4. As x approaches infinity, the value of x/4 also approaches infinity. Hence, the limit of (x^4-10)/(4x^3+x) as x approaches infinity 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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- How do you use the formal definition of a limit to find #lim 4x -1# as x approaches 2?

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