All Flashcards
What are the differences between Taylor and Maclaurin Series?
Taylor Series: Centered at any point 'a'. Maclaurin Series: Centered specifically at x=0.
What are the differences between Taylor Series and Taylor Polynomials?
Taylor Series: Infinite sum of terms. Taylor Polynomials: Finite sum of terms (partial sum).
How do you find the Taylor series for cos(3x) centered at x=0?
- Recall the Maclaurin series for cos(x). 2. Substitute 3x for x in the series. 3. Simplify the expression.
How do you find a Taylor series centered at x=a?
- Find several derivatives of f(x). 2. Evaluate the derivatives at x=a. 3. Identify a pattern. 4. Write the Taylor series using the formula.
How do you find the first four terms of a Taylor series?
- Find the general Taylor series. 2. Plug in n=0, 1, 2, and 3 into the series. 3. Simplify each term.
What is a Taylor Series?
Representation of a function as an infinite sum of terms based on its derivatives at a single point.
What is a Maclaurin Series?
A Taylor series centered at x = 0.
What is a Taylor Polynomial?
A partial sum (finite number of terms) of the Taylor series for f(x).
What is the Binomial Series?
The Taylor series for with any arbitrary value of a.