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Unformatted text preview: Suppose that we need to manufacture a metal sphere with volume 700cm 3 . If the maximum allowable tolerance in the volume is 3 ± cm 3 , then what is the maximum error that we can make in the radius of the sphere? Example: ⎩ ⎨ ⎧ = ≠ + = 1 1 , 5 , 7 2 ) ( x x x x f Suppose we want to be within 0.1 away from the value of the limit…how close should we get to 1 = x ? Formally, we want to find a small number, which we’ll call δ , so that < − < 1 x guarantees that 1 . 9 ) ( < − x f . MATH1010: Chapter 2 cont… 4 So, what is the value of δ that we should use? Now suppose we want to be within 0.01 of the limit…how close must we be to 1 = x ? Now, we could keep playing this game, requiring ) ( x f to be even closer to the limit, but the point is for us to be able to do it for any small distance away, say ε ....
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This note was uploaded on 09/13/2008 for the course MATH 1010u taught by Professor Kim during the Spring '08 term at Trinity University.
 Spring '08
 Kim
 Calculus, Derivative, Squeeze Theorem, Limits

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