lim x->∞ pow top > pow bottom
To evaluate the limit of a function as x approaches infinity, we need to compare the growth rates of the numerator and denominator in the function
To evaluate the limit of a function as x approaches infinity, we need to compare the growth rates of the numerator and denominator in the function.
In this case, we have a power function with a higher exponent in the numerator (pow top) than in the denominator (pow bottom), indicated by the notation “pow top > pow bottom”.
When the exponent in the numerator is greater than the exponent in the denominator, the function will tend towards infinity as x approaches infinity. This is because as x gets larger and larger, the term with the higher exponent will dominate and cause the overall value of the function to increase without bound.
To formally express this, we can write the limit as x approaches infinity as follows:
lim x->∞ pow top / pow bottom = ∞
In conclusion, when the exponent in the numerator is greater than the exponent in the denominator, the limit of the function as x approaches infinity is infinity.
More Answers:
Understanding the Behavior of Functions as x Approaches Infinity: A Guide to Evaluating LimitsUnleashing the Power of Limits: Evaluating Infinity with Power Functions
Asymptotic Behavior of Fractions with Power Functions: Evaluating the Limit as x Approaches Infinity