Question:

Find the limit algebraically:

Step-by-step Solution:

To find the limit of the given expression as $x$ approaches infinity, we can simplify the expression by dividing every term by the highest power of $x$ in the denominator.

Divide each term in the numerator and denominator by $x^3$:

Simplifying the expression, we get:

As $x$ approaches infinity, all terms involving $\frac{1}{x}$ and $\frac{1}{x^2}$ will tend to zero. We can ignore these terms in the numerator and denominator, yielding:

Simplifying further, we have:

Thus, the limit of the given expression as $x$ approaches infinity is $\frac{1}{2}$.