The other powers don’t matter because they’re all going to disappear. Now we have three new rules for
evaluating the limit of a rational expression as x approaches infinity.
Remember to focus your attention on the highest power of x.(1)If the highest power of x in a rational expression is in the numerator, then the limit as x
approaches infinity is infinity.Example: = ∞
(2)If the highest power of x in a rational expression is in the denominator, then the limit as x
approaches infinity is zero.Example: = 0
(3)If the highest power of x in a rational expression is the same in both the numerator and
denominator, then the limit as x approaches infinity is the coefficient of the highest term in the
numerator divided by the coefficient of the highest term in the denominator.Example:
LIMITS OF TRIGONOMETRIC FUNCTIONS
At some point during the exam, you’ll have to find the limit of certain trig expressions, usually as x
approaches either zero or infinity. There are four standard limits that you should memorize—with those,
you can evaluate all of the trigonometric limits that appear on the test. As you’ll see throughout this book,