Taylor polynomials

What is the formula for a Taylor polynomial

What is the taylor polynomial approximation

What does this mean

The 4 degree taylor polynomial centered at a=0

What significance does the 4 have

It means that you are finding the 4th degree polynomial and you cannot have x⁵, or x⁶ etc. Must be 4 or less than 4

What is the taylor remainder formula

How does the difference between x and a affect the taylor remainder formula

The closer they are to each other, the smaller the error

Which number derivative are you finding when solving for the error

The k-th plus 1 derivative

Can you error bound be negative

No, if you get a negative, you may have forgotton an absolute value sign.

what do you have to remember when finding the 3rd, 4th, or 5th… degree Taylor polynomial.

The number is the exponent on the X. Not the number of terms (n).

How should you solve integrals with the Taylor polynomial

You take the integral of the P_k,a formula (with the x’s) then you take the integral and solve

What are the steps for the finding the error of a Taylor polynomial estimation

You find the K+1 derivative and then see if it is increasing or decreasing.

You then either choose either the “K” or “a” value whichever makes the M larger (depending on if the K+1 is inc or dec)

Then you just plug in the values for Taylor Remainder Theorem equation and solve.