3/18/2009

  • Functional Approximation
    • Generalizations from Monday:

§       Polynomials centered at 0

§       Polynomials centered at some other point, x0

    • Conclusions: For any function f, any order n, any center x0
    • Practice with Taylor Polynomials
      --> Use Maple to plot the original functions and the approximations!
    • Note: Typo on #5: center should be at x0 = 1.

 

  • Accuracy Guarantees for Taylor Polynomials: How good are the approximations?
    • For Example #2, fill in the following table:

x

-2

-0.5

0

0.2

5

P1(x)

 

 

 

 

 

P3(x)

 

 

 

 

 

P5(x)

 

 

 

 

 

P7(x)

 

 

 

 

 

f(x) = sin x

 

 

 

 

 

--> Observations?  Conclusions?

  • Quiz

 

Practice Problems: Section 9.1 #7, 9, 15, 21, 23