Find the requested Taylor polynomials by using known Taylor or Maclaurin polynomials and changing variables

p3(x) for e^(3x) about x=-1

e^x about x = 0:
e^x = 1 + x + x²/2! + x³/3! + ....

e^(3x) about x = 0
e^(3x) = 1 + 3x + (3x)²/2! + (3x)³/3! + ....

e^(3x) about x = -1
=> e^(3(x+1)) about x = 0
e^(3(x+1)) = 1 + 3(x+1) + (3(x+1))²/2! + (3(x+1))³/3! + ....
e^(3x) * e³ = 1 + 3(x+1) + 9(x+1)²/2! + 27(x+1)³/3! + ....
e^(3x) = 1/e³ [1 + 3(x+1) + 9(x+1)²/2! + 27(x+1)³/3! + ....]

e^(3x) ≈ P₃(x) = 1/e³ [1 + 3(x+1) + 9(x+1)²/2 + 9(x+1)³/2]

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