Question

Use a known MacLaurin series to find the MacLaurin series of f(x)=sin(x^4) ?

Answer 1

`sin(x^4) = sum_(n=0)^oo (-1)^nx^(8n+4)/((2n+1)!)`

Explanation:

Consider the MacLaurin series of `sint`:

`sint = sum_(n=0)^oo (-1)^n t^(2n+1)/((2n+1)!)`

and let `t=x^4`:

`sin(x^4) = sum_(n=0)^oo (-1)^n(x^4)^(2n+1)/((2n+1)!)`

`sin(x^4) = sum_(n=0)^oo (-1)^nx^(8n+4)/((2n+1)!)`