Maclaurin Series
Definition
A Maclaurin series is a special case of Taylor series expansion, where the expansion is centered around x = 0 (or when h = 0).
Analogy
Imagine taking apart your favorite toy car and examining all its individual parts. The Maclaurin series is like focusing on the parts closest to the center of the car, where you can see how they contribute to its overall function.
Related terms
Binomial Series: A specific type of Maclaurin series that involves binomial coefficients and powers of x.
Taylor Polynomial: An approximation of a function using only a finite number of terms from its Taylor series.
Infinite Series: A sum of infinitely many terms, which may or may not converge to a finite value.
"Maclaurin Series" appears in:
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Practice Questions (12)
- Which term is crucial in determining the Maclaurin series for a function?
- What is the Maclaurin series for e^x?
- What is the Maclaurin series for sin(x)?
- What is the Maclaurin series for cos(x)?
- What is the Maclaurin series for ln(1 + x)?
- What is the Maclaurin series for (1 + x)^k?
- Which of the following is the first term of the Maclaurin series of $6xe^x$?
- What is the relationship between a Taylor series and Maclaurin series?
- What is the Maclaurin series for $\frac{d}{dx}e^{4x}$?
- Find the Maclaurin series for $e^{3x^2}$.
- What is the Maclaurin series for $\frac{d}{dx}cos(5x)$?
- What are the first three terms of the Maclaurin series for $e^{sin(x)}$?
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