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Top Trending Taylor Series Quizzes

Taylor & Maclaurin Series in Depth: Convergence, Radius, and Error Bounds in Applications

Taylor polynomials give us a powerful way to approximate functions by expanding them around a chosen center and capturing the behavior of their derivatives. In this quiz, you’ll work with Taylor expansions of trigonometric,...

Questions: 15 | Attempts: 11 | Last updated: Dec 15, 2025

Sample Question 1
The Taylor polynomial of degree 3 for f(x) = tan(x) centered at a = π/4 is

1 + 2(x-π/4) + 2(x-π/4)² + (8/3)(x-π/4)³

1 + 2(x-π/4) + 2(x-π/4)² + (4/3)(x-π/4)³

1 + 2(x-π/4) + (x-π/4)² + (8/3)(x-π/4)³

1 + 2(x-π/4) + 2(x-π/4)² + (⅔)(x-π/4)³

Sample Question 2
Using the 3rd-degree Taylor polynomial for tan(x) centered at π/4, approximate tan(π/4 + 0.1).

1.2227

1.2238

1.2200

1.2240

Sample Question 3
The Lagrange error bound for approximating e^{1.2} using the 4th-degree Taylor polynomial centered at 1 is at most

E^{1.2} (0.2)⁵ /120

E^{1.2} (0.2)⁴ /24

E^{1.2} (0.2)⁵ /5

E^{1.2} (0.2)³ /6

Recent Taylor Series Quizzes

From Taylor Polynomial to Taylor Series: Infinite Expansions Around a Point

Taylor series allow us to approximate functions with remarkable accuracy by expanding them into polynomials built from their derivatives at a chosen center. In this quiz, you’ll explore how Taylor and Maclaurin series...

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

Sample Question
The infinite series 1 - (0.1) + (0.1)² - (0.1)³ + ... converges to the value of which function evaluated at x=1.1?

1/x centered at 1

Ln(x) centered at 1

E^x centered at 1

1/(x-1) centered at 1

Error in Taylor Approximations: Lagrange Remainder & Alternating Series Bounds

Taylor series give us a powerful way to understand functions by expanding them into polynomials whose coefficients come directly from their derivatives. In this quiz, you’ll work with Taylor expansions centered at different...

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

Sample Question
What is the coefficient of (x-1)⁴ in the Taylor series for ln(x) centered at x=1?

-1/4

1/4

-1/3

1/3

Building Taylor Polynomials: Matching Derivatives & Approximating Function Values

Taylor series provide a powerful bridge between functions and polynomials, allowing us to approximate complicated expressions using derivatives evaluated at a single point. In this quiz, you'll dive deeper into how Taylor...

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

Sample Question
What is the Taylor series for cos(x) centered at x = 0?

∑ (-1)ⁿ x^{2n} / (2n)! from n=0 to ∞

∑ x^{2n} / (2n)! from n=0 to ∞

∑ (-1)ⁿ xⁿ / n! from n=0 to ∞

1 + x²/2! + x⁴/4! + ...

Taylor Polynomials: Local Linear & Quadratic Approximations

Taylor series allow us to express functions as infinite polynomials built from their derivatives, offering a powerful window into how functions behave near a chosen point. In this quiz, you’ll explore how individual...

Questions: 9 | Attempts: 10 | Last updated: Dec 15, 2025

Sample Question
The Taylor series for a function f centered at x = a is a power series of the form ∑ [f⁽ⁿ⁾(a)/n!] (x - a)ⁿ from n=0 to infinity. What is the coefficient of the term with (x - a)³?

F'''(a)/3

F'''(a)/3!

F(a)/6

3f'''(a)