lim x->∞ pow top < pow bottom
To evaluate the limit as x approaches infinity of a power function, you can compare the growth rates of the numerator and denominator exponents
To evaluate the limit as x approaches infinity of a power function, you can compare the growth rates of the numerator and denominator exponents.
Let’s consider the expression “pow top” divided by “pow bottom”, where “pow top” and “pow bottom” are two power functions.
If the exponent of the numerator, “pow top”, is greater than the exponent of the denominator, “pow bottom”, then as x approaches infinity, the numerator will dominate the denominator and the result will be infinity. Conversely, if the exponent of the numerator is smaller than the exponent of the denominator, then as x approaches infinity, the denominator will dominate the numerator and the result will be 0.
Mathematically, if:
– lim x->∞ pow top > pow bottom, then the limit is infinity (lim x->∞ pow top / pow bottom = ∞)
– lim x->∞ pow top < pow bottom, then the limit is 0 (lim x->∞ pow top / pow bottom = 0)
It’s important to note that when the exponents are equal (pow top = pow bottom), the limit can have various outcomes depending on the specific functions involved, as numerical coefficients and other factors need to be considered.
So, to determine the limit of “pow top” divided by “pow bottom”, compare the exponents and follow the rules outlined above for the respective cases.
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