Understanding the Limit of a Fraction as x Approaches Infinity: Rules and Examples

lim x->∞ pow top = pow bottom

To evaluate the limit of a fraction as x approaches infinity, we need to look at the highest power of x in the numerator and denominator

To evaluate the limit of a fraction as x approaches infinity, we need to look at the highest power of x in the numerator and denominator.

Let’s assume that “pow top” represents the highest power of x in the numerator, and “pow bottom” represents the highest power of x in the denominator.

If “pow top” is greater than “pow bottom,” the limit will be infinity. This is because as x becomes larger and larger, the numerator with the higher power of x will dominate the denominator, leading to an infinitely large result.

On the other hand, if “pow top” is less than “pow bottom,” the limit will be 0. In this case, as x approaches infinity, the denominator with the higher power of x will dominate the numerator, causing the fraction to approach zero.

Lastly, if “pow top” is equal to “pow bottom,” the limit can be evaluated by dividing the coefficients of the highest power terms. For example, let’s say “pow top” and “pow bottom” are both 2. In this case, we can divide the coefficient of x^2 in the numerator by the coefficient of x^2 in the denominator to determine the limit.

In summary:
– If “pow top” > “pow bottom”, the limit is infinity.
– If “pow top” < "pow bottom", the limit is 0. - If "pow top" = "pow bottom", divide the coefficients of the highest power terms to find the limit. Note: It is important to remember that these rules apply when x approaches infinity.

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