Taylor series

What is the equation of a tangent line

y= f(a)+f’(a)(x-a)

What is the second degree taylor polynomial formula

What is the taylor series formula

What are the steps for finding a taylor series

1. take the derivative of the function several times and subbing in the value of a (starting with 0, which means no derivative)

2. try to recognize a pattern from derivatives you’ve taken and make a formula for the n-th term

3. Find the formula for f⁽ⁿ⁾(a)

What do you do with the formula you derive from finding the derivative several times and pugging in “a”

You put it into the f⁽ⁿ⁾(a) part of the taylor series question

What should you do when a formula is not clear after finding multiple derivatives

You should use the expanded taylor equation which is just subbing in different n values into the original taylor equation and trying to see a pattern there

What is the taylor series for e^x

This is because any derivative of e^x is always e^x

What do you do when you are taking several derivatives and finding the equation but you don’t see the pattern for the 1st term

You find the equation for the others, then you seperate the equation for the 1st term and the equation you found for the rest of the terms

What do you need to remember when finding the derivatives of equations and trying to find the pattern and the equation for the pattern

DO NOT SIMPLIFY keep the denominator the same, add exponents negative signs, just do not simplify anything

What are the 3 ways we have to find a power series of a function