CHAPTER 1: Review of the Mathematical Foundation

Question 1

A power series that gives the expansion of a function f (x) in the neighborhood of a point a provided that in the neighborhood the function is continuous, all its derivatives exist, and the series converges to the function in which case it has the form

Answer 1

Taylor Series Expansion

Question 2

The Taylor Series, or ________, is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point.

Answer 2

Taylor Polynomial

Question 3

A _______, is a special case of the Taylor Polynomial, that uses zero as our single point.

Answer 3

Maclaurin Polynomial

Question 4

The derivative of the function f(x) evaluated at x=a gives the _______________ at x=a

Answer 4

slope of the curve

Question 5

The integral of the function f(x) over the range x=b to x=c gives the ____________ between those points

Answer 5

area under the curve