Main Concept

Given an inequality of functions of the form:

g(x)≤f(x)≤h(x)

In an interval [a,c] which encloses a point, b, the Squeeze Theorem states that if:

$\underset{x\mathit{\to }b}{\mathit{lim}}$g(x)=L=$\underset{x\mathit{\to }b}{\mathit{lim}}h\left(x\right)$

Then:

$\underset{x\mathit{\to }b}{\mathit{lim}}f\left(x\right)\mathit{\=}L$

Within the interval [a,c], the functions g(x) and h(x) are considered to be the lower and upper bounds of f(x), respectively. Thus, the limit of f(x) at point, b, can be determined graphically by finding a lower and upper bound such that:  the limits of the bounding functions at b are equal.

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