Question

Could someone help me with a few questions?

Answer 1

Say Im trying to find the taylor polynomial for
3x-cos(x)

Would I just do

\[-1[1-\frac{ x^2 }{ 2! }+\frac{ x^4 }{ 4! }...]+3x\]

Or do I need to multiply the 3x through with the -1?
I dont really understand how you can use the Taylor series of cos(x) to solve 3x-cos(x).

Also, say you had to find the taylor series of 8ln(cos(x))

Could you use the definition of the taylor series for cosine here as well, or do you need to solve for the derivatives and plug into the formula? Thanks for the help!

Answer 2

@zepdrix @agent0smith @johnweldon1993 @jhonyy9