Taylor and Maclaurin Series Concepts

To solve differential equations

To approximate functions using polynomials

To find the roots of polynomials

To calculate integrals

e^x

sin(x)

cos(x)

ln(x)

To solve algebraic equations

To find the exact value of a function

To determine the maximum value of a function

To approximate a function near a specific point

To find the derivative of a function

To solve differential equations

To estimate the error in a Taylor polynomial approximation

To calculate the exact value of a function

x = -1

x = 0

x = c

x = 1

x

1

x^2/2!

x^3/3!

x^n*n!

n^x/x!

n!/x^n

x^n/n!

e^x

sin(x)

1/(1-x)

cos(x)

1

1-x

x^2

x

Taylor series are centered at any x-value, while Maclaurin series are centered at x=0

Taylor series are only for trigonometric functions

Maclaurin series are more accurate

Taylor series are only for exponential functions