Understanding the Limit Behavior of a Function with Powers: Evaluating pow top > pow bottom as x Approaches Infinity

lim x->∞ pow top > pow bottom

To evaluate the limit of a function as x approaches infinity, we need to determine the behavior of the function as x becomes larger and larger

To evaluate the limit of a function as x approaches infinity, we need to determine the behavior of the function as x becomes larger and larger.

In the case of “pow top > pow bottom” where “pow top” and “pow bottom” represent some functions of x raised to certain powers, we can consider different scenarios:

1. If the power in the numerator (pow top) is greater than the power in the denominator (pow bottom), then the function will tend to infinity as x approaches infinity. This is because the numerator grows faster than the denominator resulting in an unbounded increase.

2. If the power in the denominator (pow bottom) is greater than the power in the numerator (pow top), then the function will tend to zero as x approaches infinity. This is because the denominator grows faster than the numerator leading to the dominance of the denominator over the numerator.

For example, let’s consider the function f(x) = x^2 / x^3 as x approaches infinity. Here the power in the numerator is 2 and the power in the denominator is 3.

Using the second scenario, we can see that the function tends to zero as x becomes larger because the denominator x^3 grows faster than the numerator x^2. As x approaches infinity, the contribution of x^3 to the overall function becomes significantly larger than x^2, causing the function to approach zero.

Hence, the limit as x approaches infinity of pow top > pow bottom depends on the specific powers involved, and the function either tends to infinity or tends to zero.

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