Make the given changes in the indicated examples of this section. Then solve the resulting problems. In Example 14, change the numerator to 4x2 + 1 and find the resulting limit.
EXAMPLE 14 Limit asx approaches infinity
We note that as x→∞ both the numerator and the denominator become large without bound. Therefore, we use a calculator (see Fig. 23.10) to make a table to see how f(x) behaves as x becomes very large:
From this table, we see that 
This limit can also be found through algebraic operations and an examination of the resulting algebraic form. If we divide both the numerator and the denominator of the function by x2which is the largest power of x that appears in either the numerator or the denominator, we have
