TOPICS
Search

Squeeze Theorem


SqueezingTheorem

The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, may be stated as follows. Let there be two functions f_-(x) and f_+(x) such that f(x) is "squeezed" between the two,

 f_-(x)<=f(x)<=f_+(x).

If

 r=lim_(x->a)f_-(x)=lim_(x->a)f_+(x),

then lim_(x->a)f(x)=r. In the above diagram the functions f_-(x)=-x^2 and f_+(x)=x^2 "squeeze" x^2sin(cx) at 0, so lim_(x->0)x^2sin(cx)=0.


See also

Limit, Pinching Theorem

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Squeeze Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SqueezeTheorem.html

Subject classifications