Select f(x) = 1/(1 - x).
1) For what values of b does the Maclaurin polynomial of degree 3 approximate f well when -b less than or equal to b?
2) What is the interval of convergence for the Maclaurin series of f(x)?
What do you notice in the graphs of the Maclaurin polynomials as n increases?
3) Consider T(x) centered at various values of a. As a varies, does the width of the interval on which Ts(x) is a close approximation change?
A) Yes
B) No
Explain.
A. The width of the interval decreases as a moves to the left and increases when a moves to the right.
B. The width of the interval increases as a moves to the left and decreases when a moves to the right.
C. The width of the interval increases as a varies.
D. The width of the interval decreases as a varies.
E. The width of the interval remains constant as a varies.
