notes_8_30_07

# notes_8_30_07 - Section 2.4 Discontinuities Section 2.5 The...

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Section 2.4 Discontinuities Section 2.5 The Pinching Theorem (Sandwich Theorem or Squeeze Theorem): Suppose that, for all x in some deleted neighborhood of c , ) ( ) ( ) ( x g x f x h . If L x h c x = ) ( lim , and , then . L x g c x = ) ( lim L x f c x = ) ( lim

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The pinching theorem is used to prove that 1 sin lim 0 = x x x for x measured in radians. See pp. 93- 94. Section 2.6 The Intermediate-Value Theorem If f is continuous on [ and K is a number between and , then there is at least one number c in the interval such that ] , b a ( a ) ( a f ) ( b f ) , b K c f = ) ( .
Example 1: Use the bisection method to estimate the value of 2 to 2 decimal places.

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