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Squeeze theorem (also called pinch theorem or sandwich theorem) is a theorem in calculus that states that if

$g(x)\le f(x)\le h(x)$

and

$\lim_{x\to a}g(x)=\lim_{x\to a}h(x)=L$

then

$\lim_{x\to a}f(x)=L$

This can be used to solve limits that would otherwise be difficult or impossible. For example, the limit

$\lim_{x\to0}x^2\sin\left(\tfrac{1}{x}\right)$

can be found because we know

$-1\le\sin\left(\tfrac{1}{x}\right)\le1$

Therefore,

$-x^2\le x^2\sin\left(\tfrac{1}{x}\right)\le x^2$

Since $\lim_{x\to0}-x^2=\lim_{x\to0}x^2=0$ , by the squeeze theorem, $\lim_{x\to0}x^2\sin\left(\tfrac{1}{x}\right)$ must also be 0.