Statement
The squeeze theorem is formally stated as follows.
Let I be an interval having the point a as a limit point. Let f, g, and h be functions defined on I, except possibly at a itself. Suppose that for every x in I not equal to a, we have:
- The functions g and h are said to be lower and upper bounds (respectively) of f.
- Here a is not required to lie in the interior of I. Indeed, if a is an endpoint of I, then the above limits are left- or right-hand limits.
- A similar statement holds for infinite intervals: for example, if I = (0, ∞), then the conclusion holds, taking the limits as x → ∞.
Read more about this topic: Squeeze Theorem
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