a. Explanation Given: The function defined by the geometric series f ( x ) = ∑ k = 0 ∞ x 2 k . Result used: The sum of the geometric series is ∑ k = 0 ∞ a r k = a 1 − r if | r | < 1 and does not exists if | r | ≥ 1 . Calculation: From the Result, the geometric series defined only by f ( x ) = ∑ k = 0 ∞ x 2 k when the ratio x 2 is less than 1, which means | x | < 1 . Compute the function f ( x ) = ∑ k = 0 ∞ x 2 k at x = 0 . Here, | x | < 1 and the first term a = 1 . Thus, by Result stated above f ( 0 ) = 1 1 − 0 2 . f ( 0 ) = 1 Compute the function f ( x ) = ∑ k = 0 ∞ x 2 k at x = 0.2 . Here, | x | < 1 and the first term a = 1 . Thus, by Result stated above f ( 0.2 ) = 1 1 − 0.2 2 . f ( 0.2 ) = 1 1 − 0.4 = 1 0.6 = 10 6 That is, f ( 0 b. To determine To find: The domain of f .

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8.3, Problem 96E

To determine

To evaluate: The values of f(0),f(0.2),f(0.5),f(1) and f(1.5) if possible.

To determine

To find: The domain of f.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 95E

Chapter 8.3, Problem 97E

Students have asked these similar questions

Use a graphing utility to graph the function.Determine the horizontal asymptote for the graph of f and discuss its relationship to the sum of the given series.

Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) If lim an + 0 then, the sequence {an} is divergent. (b) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 > ca, is also divergent. n=1 (c) Let s, = a1 +... + an. If lim s, = 0, then the series >a, is convergent. n +00

use A=200

Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

Additional Math Textbook Solutions

Find more solutions based on key concepts

To write a real-world problem involving an inequality and negative numbers where the inequality symbol won’t re...

Glencoe Math Accelerated, Student Edition

1. On a real number line the origin is assigned the number _____ .

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Find the first four nonzero terms of the Taylor series for the functions in Exercises 1–10. 1. (1 + x)1/2

University Calculus: Early Transcendentals (3rd Edition)

In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 37.

Precalculus

The given statement is true or false: “A function is a relation between two sets D and R so that each element x...

Precalculus

Suppose that the graph of a function f is known. Then the graph of y=f( x2 ) may be obtained by a(n) ______ shi...

Precalculus (10th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The values of f ( 0 ) , f ( 0.2 ) , f ( 0.5 ) , f ( 1 ) and f ( 1.5 ) if possible.

Solution Summary: The author evaluates the geometric series f(x)=displaystyle undersetk=0overset