substitute a letter for 3x; for example, a. Now, we get the following:
= 3(1) = 3
Example 12: Find .
Now we get a bit more sophisticated. First, divide both the numerator and the denominator by x, like so
Next, multiply the top and bottom of the numerator by 5, and the top and bottom of the denominator by 4,
which gives us
From the work we did in Example 11, we can see that this limit is .
Guess what! You have two more rules!
Rule No. 3: = aRule No. 4: Example 13: Find .
Using trigonometric identities, you can replace (1 − cos^2 x) with sin^2 x.