Lesson 1: Review of the Math Foundation

Question 1

The _____________ of the function f(x) evaluated at x=a gives the slope of the curve at x=a.

Answer 1

derivative

Question 2

The ___________ of the function f(x) over the range x=b to x=c gives the area under the curve between those points.

Answer 2

integral

Question 3

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

Answer 3

Taylor Series Expansion

Question 4

where ________ is the derivative of the nth order of f(x) evaluated at a.

Answer 4

f^n (a)

Question 5

The _____________, 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 5

Taylor Series, Taylor Polynomial

Question 6

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

Answer 6

Maclaurin Polynomial