lim x->∞ pow top < pow bottom
To find the limit of a function as x approaches infinity (denoted as lim x->∞), we need to determine the behavior of both the numerator (pow top) and the denominator (pow bottom) as x becomes very large
To find the limit of a function as x approaches infinity (denoted as lim x->∞), we need to determine the behavior of both the numerator (pow top) and the denominator (pow bottom) as x becomes very large.
If the power of x in the numerator is smaller than the power of x in the denominator, then the limit as x approaches infinity will be 0. This is because, as x gets larger and larger, the effect of the numerator becomes negligible compared to the denominator.
For example, let’s consider the function f(x) = x^2 / x^3 as x approaches infinity. Here, the power of x in the numerator (2) is smaller than the power of x in the denominator (3).
As x becomes very large, x^2 grows at a slower rate than x^3. So, if we divide x^2 by x^3, the result tends to become smaller and smaller as x approaches infinity.
Mathematically, we can use the following steps to evaluate the limit:
lim x->∞ (x^2 / x^3) = lim x->∞ (1 / x)
Since the power of x in the denominator is larger than the power of x in the numerator, as x approaches infinity, the expression 1 / x approaches 0. Hence, the limit as x approaches infinity for the given function is 0.
Please note that the same logic applies to any function where the power of x in the numerator is smaller than the power of x in the denominator. The limit will always be 0 as x approaches infinity.
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