Question

Find the Maclaurin expansion of cos(x^3)

Answer 1

So i'm thinking since it's Maclaurin a = 0.
I know the Maclaurin expansion of cos(x) = SUM(-1)^n * (x^(2n))/(2n)!

Answer 2

replace x with x^3

Answer 3

why would we just do that ? if it was asking for the maclaurin expansion of x cos (x) i would just multiply the expansion of cos(x) by x. So wouldn't I need to multiply it by something again or do some computation to the orignal expansion besides just replacing x ?

Answer 4

just replacing

Answer 5

for example u know that \( \frac{1}{1-x}=1+x+x^2+... \) for |x|<1 now for \( \frac{1}{1-x^2}\) u just need to replace x with x^2 to get \( \frac{1}{1-x^2}=1+x^2+x^4+... \)

Answer 6

oh wow. I get it now. sorry for making you have to type up those equations. Thanks though!

Answer 7

welcome my friend