Maclaurin Series Quizzes, Questions & Answers

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Maclaurin Series from Differential Equations: Modeling with sin, cos, sinh, cosh & Beyond

Maclaurin series allow us to zoom in on functions and reveal their hidden structure through infinite power expansions. In this quiz, you'll explore how differentiation, substitution, and algebraic manipulation transform...

Questions: 15 | Attempts: 23 | Last updated: Dec 15, 2025

Sample Question 1
Which of the following is the Maclaurin series representation of cos(x)?

N=0 (-1)ⁿ x^(2n+1)/(2n+1)!

N=0 (-1)ⁿ x²n/(2n)!

N=0 x^(2n+1)/(2n+1)!

N=0 x²n/(2n)!

Sample Question 2
Find the Maclaurin series for f(x) = 1/(1-x)² by differentiating the geometric series.

N=0 n * xⁿ⁻¹

N=0 xⁿ

N=0 (-1)ⁿ * n * xⁿ⁻¹

N=0 xⁿ⁺¹ / (n+1)

Sample Question 3
Find the Maclaurin series for ln(1-x).

N=1 (-1)ⁿ xⁿ/n for |x| < 1

-n=1 xⁿ/n for |x| < 1

N=0 (-1)ⁿ xⁿ/n for |x| < 1

N=0 xⁿ/n for |x| < 1

Recent Maclaurin Series Quizzes

Maclaurin Series in Depth: Error Bounds, Limits & Series-Based Approximations

Maclaurin series offer a powerful lens for understanding how functions behave near zero—turning exponentials, trig functions, logarithms, and rational expressions into infinite polynomials whose patterns reveal deep...

Questions: 15 | Attempts: 10 | Last updated: Dec 15, 2025

Sample Question
What is the Maclaurin series for f(x) = 1/(2+x)?

N=0 (-1)ⁿ xⁿ / 2ⁿ⁺¹

N=0 (-1)ⁿ xⁿ / 2ⁿ

N=0 xⁿ / 2ⁿ⁺¹

N=0 (-1)ⁿ 2ⁿ xⁿ

Building New Maclaurin Series: Substitution, Products, Integration & Differentiation

Maclaurin series provide one of the most powerful ways to understand and approximate functions by expressing them as infinite sums centered at zero. In this quiz, you'll explore how classic functions—like exe^xex,...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
What are the first four terms of the Maclaurin series for eˣ?

1 + x + x²/2 + x³/6

1 + x + x² + x³

1 + x + x²/2! + x³/3!

Both A and C are correct

Approximating Functions with Maclaurin Series: eË£, sin x, cos x, ln(1+x), arctan x

Maclaurin series transform familiar functions into powerful infinite expansions, revealing patterns that make calculus, approximation, and analysis far more intuitive. In this quiz, you’ll explore the core series every...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
Which represents the Maclaurin series for 1/(1-x)?

Σ from n=0 to infinity of xⁿ

Σ from n=0 to infinity of (-x)ⁿ

Σ from n=0 to infinity of xⁿ / n!

Σ from n=0 to infinity of (-1)ⁿ x^(2n)

Maclaurin Series Basics: Key Expansions & Geometric Links

Maclaurin series lie at the heart of mathematical approximation, turning complex functions into elegant infinite polynomials. In this quiz, you’ll explore how functions like exe^xex, sinâ�¡xsin xsinx, and cosâ�¡xcos...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
What is the Maclaurin series for eˣ?

(-1)ⁿ x^(2n) / (2n)!

N=0 x^(2n) / (n!)