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.
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:
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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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