This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 = ex^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...
View
Full Document
 Spring '08
 Muralee
 Calculus, Approximation, Derivative, quadratic approximation, JP Rodriguez Prof., JP Rodriguez, finda quadratic polynomial

Click to edit the document details