Series to functions Find the function represented by the following series and find the interval of convergence of the series. (Not all these series are power series.) 63. ∑ k = 0 ∞ ( x − 2 ) k
Series to functions Find the function represented by the following series and find the interval of convergence of the series. (Not all these series are power series.) 63. ∑ k = 0 ∞ ( x − 2 ) k
Solution Summary: The author explains the function represented by the given series and interval of convergence.
Series to functionsFind the function represented by the following series and find the interval of convergence of the series. (Not all these series are power series.)
2. Find the interval of convergence for the Maclaurin series for the function of f(x)= sin(x)
a) Find the Maclaurin series for sin(x):
b) Apply the Ratio Test: (Form the fraction |an+1| / |an| and simplify as much as possible)
c) Evaluate the limit:
d) Find the interval of convergence:
HINT: Recall that the limit needs to be less than 1
Power series for derivativesa. Differentiate the Taylor series centered at 0 for the following functions.b. Identify the function represented by the differentiated series.c. Give the interval of convergence of the power series for the derivative.
ƒ(x) = (1 - x)-1
Maclaurin and Taylor series: Find the indicated Maclaurin or Taylor series for the given function about the indicated point, and find the radius of convergence for the series.
Chapter 9 Solutions
Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)
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