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Do you mean the idea of a squeeze theorem?
An example is when trying to find lim x-> 0 of sinx/x.
If you look through a basic proof, you'll end up with the inequality,
Lim x->0 1>sinx/x > cosx
As x goes to zero, 1 stays fixed but cosx goes to 1. Because sinx/x is always between 1 and cosx, sinx/x MUST go to 1 as well...it gets squeezed by 1 and cosine.
Does this help?
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kind of but how did you know to squeeze sinx/x between 1 and cosx? (like how do you know what numbers to squeeze it with?
That comes from a geometric setup where a triangle is inscribed within a sector of a circle which is inscribed (in turn) within a right-angled triangle. I can't find a picture, but it's usually something covered in school.
Usually, we try to find relations between sizes of things, with the thing we want to squeeze having magnitude somewhere between the first and last. We also operate on the understanding that we want to set up our 'first' and 'last' so that they will tend to the same value in the limit...this forces (logically) the limit in between to be the same.
I hope this helps. It would be good if this site had a drawing tool. I can't find links to useful sites either.