AP®︎ Calculus BC: Topic 10.11 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 10.11 of AP Calculus BC – Finding Taylor Polynomial Approximations of Functions.
Questions List
Topic 10.11
Question 1 Easy
Let be an integer, and suppose has derivatives through order at . In the nth-degree Taylor polynomial for about , which expression gives the coefficient of ?
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 10.11: Finding Taylor Polynomial Approximations of Functions
Learning Objective: LIM-8.A
Represent a function at a point as a Taylor polynomial.
Essential Knowledge: LIM-8.A.1
The coefficient of the nth degree term in a Taylor polynomial for a function f centered at x = a is f^(n)(a)/n!.
Essential Knowledge: LIM-8.A.2
In many cases, as the degree of a Taylor polynomial increases, the n-th degree polynomial will approach the original function over some interval.
Learning Objective: LIM-8.B
Approximate function values using a Taylor polynomial.
Essential Knowledge: LIM-8.B.1
Taylor polynomials for a function f centered at x = a can be used to approximate function values of f near x = a.
