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Maclaurin Series
Find derivatives
Plug in x = 0
Multiple by x^n and divide by n!
Maclaurin Series: 1/(1-x)
1 + x + x² + x³ … + x^n
Geometric Series: geometry is simple, just add x
Taylor Series
Find derivatives of function
Use x = c in derivatives
Multiply by (x-c)^n and divide by n!
Maclaurin Series: e^x
1 + x + x² /2! + x³/3! … x^n/n!
Exponential Series: exponents match factorials
Maclaurin Series: sin x
x - x³/3! + x^5/5! - x^7/7! …
Sin starts with x, switches signs, and is sinisterly odd
Maclaurin Series: cos x
X - x²/2! + x^4/4! - x^6/6! …
Cos starts with x, switches signs, and commonly even
Parametric and Cartesian Conversians