## lim x->∞ pow top = pow bottom

### To evaluate the limit as x approaches infinity of a fraction with a power on the numerator and denominator, we need to consider the exponents on the terms

To evaluate the limit as x approaches infinity of a fraction with a power on the numerator and denominator, we need to consider the exponents on the terms.

Let’s consider the given expression: lim(x->∞) pow(top) / pow(bottom).

There are three possible scenarios to consider:

1. If the exponent on the numerator (pow(top)) is greater than the exponent on the denominator (pow(bottom)), then the limit will tend to infinity.

Example: lim(x->∞) x^2 / x = lim(x->∞) x^(2 – 1) = lim(x->∞) x = ∞

2. If the exponent on the numerator (pow(top)) is less than the exponent on the denominator (pow(bottom)), then the limit will tend to zero.

Example: lim(x->∞) x / x^2 = lim(x->∞) x^(1 – 2) = lim(x->∞) 1/x = 0

3. If the exponent on the numerator (pow(top)) is equal to the exponent on the denominator (pow(bottom)), then we can simplify the expression and evaluate the limit.

Example: lim(x->∞) x^2 / x^2 = lim(x->∞) 1 = 1

In summary, the limit of pow(top) / pow(bottom) as x approaches infinity depends on the relative exponents of the numerator and denominator. If the exponent on the numerator is greater, the limit tends to infinity. If the exponent on the denominator is greater, the limit tends to zero. And if the exponents are equal, the limit is a constant value.

## More Answers:

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