Essential Knowledge 1.1D2

Essential Knowledge 1.1D2 Students will know that relative magnitudes of functions and their rates of change can be compared using limits.

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While you could understand these concepts with just your knowledge of limits, you'll want to wait until you've learned derivatives (particularly L'Hôpital's Rule) before looking at this objective. There are simply too many questions that require L'Hôpital's Rule.

In fact, I don't think I'm going to spend too much time on this. The idea is the same as L'Hôpital's Rule. If you want to compare 2 functions,

1. make a fraction with one as the numerator and one as the denominator,

2. take the derivative of the numerator and denominator separately

   1. If the fraction goes to infinity, the numerator won, so the numerator is increasing at a larger rate

   2. If the fraction goes to 0, the denominator won, so the denominator is increasing at a larger rate

   3. If you get a number, that number tells you how many times faster the numerator in increasing compared to the denominator