
Understanding Power Series and Arctangent

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard

Lucas Foster
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main goal of the video tutorial?
To explore the history of power series.
To find the power series approximation of arctangent of 2x centered at zero.
To solve a complex integral involving arctangent.
To derive the formula for the derivative of arctangent.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of arctangent of 2x?
1 over 1 plus x squared
2 over 1 plus 4x squared
1 over 1 plus 4x squared
2 over 1 plus x squared
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the function g(x) introduced?
To solve a different problem.
To find the integral of arctangent.
To complicate the problem further.
To make the derivative calculations easier.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expression for g(x)?
1 over 1 plus x
1 over 1 plus x squared
1 over 1 plus 4x squared
1 over 1 plus 2x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is made in the power series of g(x) to find f(x)?
Replace x with 4x squared
Replace x with 2x
Replace x with x squared
Replace x with 8x squared
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first term in the power series of f(x) after substitution?
2
4
8
16
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of integrating the power series of f(x)?
To find the power series of arctangent of 2x.
To find the derivative of arctangent of 2x.
To solve a differential equation.
To determine the convergence of the series.
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