Taylor Polynomials and Error Bounds

Taylor Polynomials and Error Bounds

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Hard

Created by

Thomas White

FREE Resource

This video tutorial covers multiple choice problems for AP Calculus BC, focusing on calculator-active problems. It includes solving the area between polar curves, using Euler's method for differential equations, calculating arc length, finding average value in polar coordinates, using Taylor polynomials for approximation, and understanding Lagrange error bound. The session is led by teachers Brian Passwater and Tony Recer, who guide through each problem with detailed explanations and calculator demonstrations.

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19 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Who are the instructors for this AP Calculus BC session?

Michael Scott and Dwight Schrute

Brian Passwater and Tony Recer

John Doe and Jane Smith

Alice Johnson and Bob Brown

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first problem about in this session?

Calculating the area between two polar curves

Using Euler's method

Taylor polynomial approximation

Finding the arc length of a curve

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which two polar curves are used in the first problem?

R = 5 - 4 sine Theta and R = 3 sine Theta

R = 4 - 3 cosine Theta and R = 5 cosine Theta

R = 2 - cosine Theta and R = 4 cosine Theta

R = 3 + 2 sine Theta and R = 6 sine Theta

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the key concept used to find the area between the polar curves?

Slope of the curves

Integral of the curves

Derivative of the curves

Intersection of the curves

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Euler's method, what is the initial condition given?

F(1) = 7

F(0) = 5

F(2) = 3

F(3) = 9

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many steps are used in Euler's method for this problem?

Five steps

Four steps

Three steps

Two steps

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of using Euler's method in this problem?

To approximate F(0)

To find the exact value of F(0)

To calculate the derivative at F(0)

To determine the integral of F(0)

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