# How to evaluate a limit to infinity

the calculator answer of 0.5 is very convincing, but it’s not mathematically rigorous, so if you stop there, the math police may get you. Try substitution — always a good

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## Calculus I

Now let us look into some example problems on evaluating limits at infinity. Question 1 : lim x-> ∞ (x 3 + x)/(x 4 - 3x 2 + 1) Solution : f(x) = (x 3 + x)/(x 4 - 3x 2 + 1) Divide each terms by x 4, we

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## Limits at Infinity

The limit approaches zero if the function is heavy at the bottom or if the degree of the denominator exceeds that of the numerator. The limit approaches a constant value if the

## Infinite Limits

In order to evaluate this limit, we will divide the numerator and the denominator by the highest power of x x in the denominator. Since terms of the form \frac {1} {x^2} x21

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3.5 Limits at Infinity, Infinite Limits and Asymptotes

lim x→∞ ( 1 x) = 0. In other words: As x approaches infinity, then 1 x approaches 0. When you see limit, think approaching. It is a mathematical way of saying we are not talking about when

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