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Unformatted text preview: a, b, and x, we can finally plug these three values into f ( a ) and p ( a ) and set both functions equal to one another. ax 2 + bx + c = e-x^2 (-1)(0) 2 + (0)(0) + c = e-(0)^2 0 + 0 + c = 1 c = 1 Now that we have values for a, b, and c, we can plug it into p ( x ) to get: p ( x ) = ax 2 + bx + c p ( x ) = (-1) x 2 + (0) x + 1 p ( x ) = -x 2 + 1 And that is our quadratic approximation for f ( x ). B) On separate sheet C) Use the function p to approximate the value of f at x = ½ and x = 2 p ( 1/2 ) = -(1/2) 2 + 1 = (1/4) + 1 = 1.25 p ( 2 ) = -(2) 2 + 1 = -4 + 1 = -3 D) For values of a near x = 0, p ( x ) is a good approximation of f ( x ), but as values for a move farther from 0 (in either direction), p ( x ) becomes a progressively worse approximation...
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This note was uploaded on 04/13/2008 for the course MATH 021 taught by Professor Muralee during the Spring '08 term at Lehigh University .
- Spring '08