AP®︎ Calculus BC: Topic 10.13 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 10.13 of AP Calculus BC – Radius and Interval of Convergence of Power Series.
Questions List
Topic 10.13
Question 1 Easy
Which of the following is a power series in ?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Topic 10.13: Radius and Interval of Convergence of Power Series
Learning Objective: LIM-8.D
Determine the radius of convergence and interval of convergence for a power series.
Essential Knowledge: LIM-8.D.1
A power series is a series of the form Σ_{n=0}^∞ a_n r^n, where n is a non-negative integer, {a_n} is a sequence of real numbers, and r is a real number.
Essential Knowledge: LIM-8.D.2
If a power series converges, it either converges at a single point or has an interval of convergence.
Essential Knowledge: LIM-8.D.3
The ratio test can be used to determine the radius of convergence of a power series.
Essential Knowledge: LIM-8.D.4
The radius of convergence of a power series can be used to identify an open interval on which the series converges, but it is necessary to test both endpoints of the interval to determine the interval of convergence.
Essential Knowledge: LIM-8.D.5
If a power series has a positive radius of convergence, then the power series is the Taylor series of the function to which it converges over the open interval.
Essential Knowledge: LIM-8.D.6
The radius of convergence of a power series obtained by term-by-term differentiation or term-by-term integration is the same as the radius of convergence of the original power series.
