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Series--Every Day Questions
Questions to ask yourself every day for series.
10
Mathematics
02/15/2021

Term
 What is an nth order Taylor Polynomial generated by f(x) at x=a?
Definition
 An nth order Taylor Polynomial generated by f(x) at x=a is a polynomial that shares the same y-coordinate and the same first n derivatives as f(x) at x=a.
Term
 What is a Taylor Polynomial used for?
Definition
 A Taylor Polynomial is used to approximate a function. It's like a tangent line on steroids.
Term
 What is the difference between a Taylor Polynomial and a Taylor Series
Definition
 A Taylor Polynomial has a finite number of terms. A Taylor Series has an infinite number of terms.
Term
 What is a Taylor Series?
Definition
 A Taylor Series is a power series that converges to a function on some interval of x.
Term
 What information do you get from a Taylor Series?
Definition
 You get the y-coordinate and an infinite number of derivatives of f(x) at x=a.
Term
 What is the nth derivative (at the center) of [image]?
Definition
 The nth derivative of this series is 1.
Term
 What is a Maclaurin Series?
Definition
 A Maclaurin Series is a Taylor Series centered at 0.
Term
 How do you use a Taylor Polynomial to approximate a function?
Definition
 Find the equation of the desired Taylor Polynomial, then substitute the value of x.
Term
 What is the relationship between a tangent line at x=a and a Taylor Series at x=a?
Definition
 The tangent line is equivalent to the first order Taylor Polynomial.
Term
 What are the six methods for creating a power series that converges to a function?
Definition
 1) Use the sum of a geometric series.2) Differentiate a convergent series.3) Integrate a convergent series.4) Substitute an expression of x for x.5) Multiply (or divide) by an expression of x.6) Use the Taylor Series general term to create a Taylor series from scratch.
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