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Solved: Functions defined as series Suppose a function f
Chapter 11, Problem 80AE(choose chapter or problem)
Functions defined as series Suppose a function f is defined by the geometric series \(f(x)=\sum_{k=0}^{\infty} x^{2 k}\)
a. Evaluate f(0), f(0.2), f(0.5), f(1), and f(1.5).
b. What is the domain of f?
Questions & Answers
QUESTION:
Functions defined as series Suppose a function f is defined by the geometric series \(f(x)=\sum_{k=0}^{\infty} x^{2 k}\)
a. Evaluate f(0), f(0.2), f(0.5), f(1), and f(1.5).
b. What is the domain of f?
ANSWER:Problem 80AEFunctions defined as series Suppose a function f is defined by the geometric series .a. Evaluate f(0), f(0.2), f(0.5), f(1), and f(1.5).b. What is the domain of fSolution Step 1In this problem we have to evaluate f(0), f(0.2), f(0.5), f(1) and f(1.5) if possible and we have to find the domain of where We know that “If then the sum of the infinite geometric series is If then the series diverges.”We have Here Hence if