CalcNotes0206-page8

CalcNotes0206-page8 - lim x ± a B x = L and lim x ± a T x...

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(Section 2.6: The Squeeze (Sandwich) Theorem) 2.6.8 PART B: THE SQUEEZE (SANDWICH) THEOREM We will call B the “bottom” function and T the “top” function. The Squeeze (Sandwich) Theorem Let B and T be functions such that Bx () ± fx () ± Tx () on an open x -interval containing a , except possibly at a itself. If lim x ± a Bx () = L , and lim x ± a Tx () = L , where L is a real constant, then lim x ± a fx () = L . Variations for One-Sided Limits • To show that lim x ± a + fx () = L , we show that
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Unformatted text preview: lim x ± a + B x ( ) = L , and lim x ± a + T x ( ) = L , and we require B x ( ) ± f x ( ) ± T x ( ) on an x-interval of the form a , c ( ) for some real constant c , where c > a . • To show that lim x ± a ² f x ( ) = L , we show that lim x ± a ² B x ( ) = L , and lim x ± a ² T x ( ) = L , and we require B x ( ) ± f x ( ) ± T x ( ) on an x-interval of the form c , a ( ) for some real constant c , where c < a ....
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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