Final answer:
To find the limit as x approaches infinity of ln(x²) / (x² * x), we can apply L'Hopital's Rule. The limit is 0.
Step-by-step explanation:
To find the limit as x approaches infinity of ln(x²) / (x² * x), we can apply L'Hopital's Rule. L'Hopital's Rule states that if we have an indeterminate form of the type 0/0 or ∞/∞, we can differentiate the numerator and denominator separately and then take the limit again.
Applying L'Hopital's Rule to this problem, we differentiate the numerator ln(x²) with respect to x, which gives 2/x. We differentiate the denominator (x² * x) with respect to x, which gives 3x². Taking the limit as x approaches infinity of the new fraction 2/x / (3x²), we again apply L'Hopital's Rule and differentiate the numerator and denominator to get 2/3x / 6x.
Finally, taking the limit as x approaches infinity of the latest fraction 2/3x / 6x, we find that the limit is 0. Therefore, the limit as x approaches infinity of ln(x²) / (x² * x) is 0.