MacLaurin series i don't understand this, so please help me?

Question

obtain the first 4 terms in the MacLaurin series for e^-X2

i really have no idea. what should i do first? please help me, i haven't learned this yet and i need to know.

Anonymous · Accepted Answer

Effectively you keep differentiating to get the next function and sub in 0...:

f(x) = e^(-2x): 
when x=0, f(x) = 1

f'(x) = -2e^(-2x) [first derivative] 
when x=0, f'(x) = -2

f''(x) = 4e^(-2x) [second derivative]
when x=0, f''(x) = 4

f''(x) = -8e^(-2x) [third derivative]
when x=0, f''(x) = -8

f''(x) = 16e^(-2x) [fourth derivative]
when x=0, f''(x) = 16

so.. e^(-2x) = 1  + -2x/1! + 4x^2/2! + -8x^3/3! + 16x^4/4!
The numbers before the x's are the stuff we worked out above followed by x of an increasing power and divided by an increasing factorial

so e^(-2x) = 1 - 2x + 2x^2 - 4/3 x^3 + 2/3 x^4

MacLaurin series> i don't understand this, so please help me?

1 Answer