## lim x->∞ pow top < pow bottom

### To find the limit as x approaches infinity of a power function, we need to compare the exponents of the numerator and denominator

To find the limit as x approaches infinity of a power function, we need to compare the exponents of the numerator and denominator. Let’s denote the power of the top function as p and the power of the bottom function as q.

If p < q, then the limit as x approaches infinity of the power function is 0. This is because as x becomes infinitely large, the denominator will grow much faster than the numerator, effectively making the fraction very small. If p = q, then the limit as x approaches infinity of the power function will be the ratio of the coefficients of the highest power terms in the numerator and denominator. For example, if our function is (5x^3 + 2x^2 + 3) / (2x^3 + 4x + 1), the limit would be 5/2. This is because the highest power term in the numerator is 5x^3 and in the denominator is 2x^3, so their ratio is 5/2. If p > q, then the limit as x approaches infinity of the power function is infinity or negative infinity, depending on the signs of the coefficients. This is because as x becomes infinitely large, the numerator will grow much faster than the denominator, resulting in a very large positive or negative number.

It is important to note that these rules apply only for power functions when x approaches infinity. Other types of functions may have different rules for determining the limit.

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