Taylor Series
Definition
A Taylor series is an expansion of a function into an infinite sum of terms, where each term represents the contribution from different derivatives of the function at a specific point.
Analogy
Think of baking cookies from scratch. The Taylor series is like breaking down the recipe into individual ingredients and their quantities, allowing you to recreate the entire batch by adding up these separate components.
Related terms
Power Series: A special type of Taylor series where each term involves powers (exponents) of x.
Radius of Convergence: The distance from the center point at which a power series converges to its original function.
Remainder Estimation Theorem: A theorem used to estimate how closely an approximation using only some terms in a Taylor series matches the actual function.
"Taylor Series" appears in:
Study guides (3)
Additional resources (1)
Practice Questions (10)
- What is the Taylor series for the function f(x) centered at x = 0?
- When is a Taylor series representation of a function considered accurate?
- Which mathematical concept is used to construct the Taylor series of a function?
- What does the remainder term represent in a Taylor series approximation?
- What is the Taylor series for f(x) centered at x = a?
- How can the Taylor series be used to approximate the value of a function?
- What is the Taylor series for f(x) centered at x = 0 called?
- Which term in a Taylor series represents the linear approximation of a function?
- Which condition must be satisfied for a Taylor series to converge to the function?
- What is the relationship between a Taylor series and Maclaurin series?
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