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# Sandwich Theorem

Sandwich theorem is also known as squeeze theorem.

Sandwich Theorem

Sandwich theorem is also known as squeeze theorem. As shown in the figure 9.27, if f(x) is ‘squeezed’ or ‘sandwiched’ between g(x) and h(x) for all x close to x0, and if we know that the functions g and h have a common limit l as xx0 , it stands to reason that f also approaches l as xx0 .

Theorem 9.5 (Sandwich Theorem)

If f , g, h : I R→R such that g ( x) ≤ f ( x) ≤ h ( x) for all x in a deleted neighbourhood of x0 contained in I, and if

We could have wrongly concluded had we resorted to applying the limit theorems, namely

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11th Mathematics : UNIT 9 : Differential Calculus Limits and Continuity : Sandwich Theorem | Definition, Solved Example Problems | Mathematics