A Limit That Fails, and a Wall That Is Not Always There

You'll learnto read an infinite limit as a limit that fails and a description of how, to get the direction of each side from the sign of the bottom, and to tell a wall from a hole before claiming either.

Near a wall the outputs do not settle on anything; they leave. Writing that the limit is infinite records which way they left, and it is not a claim that a limit exists. The two sides can leave in opposite directions, and a zero underneath is not always a wall at all. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · UNBOUNDED IS A WAY OF FAILING · v2

a surviving factor is a wall, a canceling factor is a hole, and unbounded is not a value

Before you start

What you're looking at

One graph at a time. A dashed vertical rule marks a wall; a hollow ring marks a hole. Amber walks in from the left and violet from the right.

The question

Where do the outputs go on each side, and is a zero underneath enough to put a wall there?

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