Section 6.2 Limits of the form zero over zero: Consider limits of difference quotients #48
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Section 6.2 Limits of the form zero over zero: Consider limits of difference quotients
The last two examples, involving the limit of (1/(x+1) - 3/(x+5))/(x-1) and the limit of (sqrt(x+5)-2)/(x+1) are difficult examples, and they will not show up again in the book. But they are comparable in form and to the limits that one would compute when computing the f'(x) or f'(c) for f(x) = 1/(x+5) or f(x) = sqrt(x+5). I suggest that in Section 6.2, you use limits that will also appear in future sections when computing derivatives. That way, students will get to see the same hard limit more than once.
(In fact, I would suggest breaking Section 6.2 into two sections, with the second section devoted to the limits of difference quotients.)