Choosing a Limit Procedure

You'll learnto open every limit by substituting, to sort what comes back into a number, a zero over zero, or a nonzero over zero, and to let that sorting choose the next move.

You now have every technique in the unit, so the work is no longer doing one but choosing one. Put the number in and read what comes back: a number is the answer, zero over zero means rewrite, and a nonzero over zero means the outputs run away. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · SUBSTITUTE FIRST, THEN READ THE FORM · v2

substitute first · a number stops · 0/0 rewrites · k/0 runs away

Before you start

What you're looking at

One graph with one target at x = 2, and three different functions drawn on it in turn; only what happens at the target changes.

The question

Substituting is always the first move, so which of the three things it can return is this one, and what does it tell you to do next?

Step 1 / 12