Example 8: Find .
When you have variables in both the top and the bottom, you can’t just plug ∞ into the expression. You’ll
get . We solve this by using the following technique:
When an expression consists of a polynomial divided by another polynomial, divide each term of the
numerator and the denominator by the highest power of x that appears in the expression.
The highest power of x in this case is x^1 , so we divide every term in the expression (both top and bottom)
by x, like so
Now when we take the limit, the two terms containing x approach zero. We’re left with .
Example 9: Find .
Divide each term by x^2 . You get
Example 10: Find .
Divide each term by x^10.