Two Bounds, and Whether the Space Between Them Closes

You'll learnto check both parts of the Squeeze Theorem separately, to build bounds by multiplying an inequality through, to notice when a bound holds on one side only, and to say nothing when the two bounds disagree.

Some functions have no limit of their own and still sit between two functions that do. If the outer two close on the same value, the middle one has nowhere else to go. The idea is easy; the marks are lost on the checking. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · BOTH BOUNDS MUST MEET · v2

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Before you start

What you're looking at

One graph. Two green curves are the bounds, the shaded strip between them is where the middle function is allowed to be, and the pink curve is trapped there.

The question

Does the strip close on a single height as the inputs close in on the target, and does the inequality hold on both sides?

Step 1 / 12