general question on taylor and malcaurin series. Why is fourth order of sinx = x - x^(3)/3! only two terms while fourth order of 1/(1+x) = 1-x+x^2-x^3+x^4 has 5 tems? Is it because we dont' include terms with an x^? greater than 4 and sin is one of the odd functions that it doesn't have a 1, x^2,, or x^4 term?

Question

general question on taylor and malcaurin series.  Why is fourth order of sinx = x - x^(3)/3! only two terms while fourth order of 1/(1+x) = 1-x+x^2-x^3+x^4 has 5 tems? Is it because we dont' include terms with an x^? greater than 4 and sin is one of the odd functions that it doesn't have a 1, x^2,, or x^4 term?

ganeshie8 · Answer

$\sin x  = x -  0.\frac{x^2}{2!} - \frac{x^3}{3!} +  0.\frac{x^4}{2!} +  \frac{x^5}{5!} + ... $

amistre64 · Answer

the fourth order polynomial can be written with zero coefficients .... im getting slower in my old age lol

ganeshie8 · Answer

if you take oly up to 4th order terms, u wil get oly two terms

anonymous · Answer

when the say 4th degree in a book is that interchangeable with 4th order?

ganeshie8 · Answer

yes degree and order are used interchangeably mostly

anonymous · Answer

okay thank you

ganeshie8 · Answer

when talking about polynomials ofc :)