Maclaurin series

Question

The Maclaurin series for f(x)=cos(x) is given by (fill in the blanks below):

cos(x)= __ +__x + __/(2x²) + ____/(6x³) + ____/(24x⁴)

How does these types of equation works, i get that we differentiate the equation and then plug in equations butt like when implying d/dx(cos(x)) = -sin(x) but then how is it converted in to fraction like ___/2x² and so on.

Answer 1

Your question has so many mistakes it is nearly impossible to answer.

The Maclaurin series for cos x=1-(x²/2)+(x⁴/24)...(-1)^k(x^2k/(2k)!).

Your English grammar is so bad that I am reluctant even to try to answer your question.

Suffice it to say that the Maclaurin series in general is

f(x)=f(0)+xf'(0)+[x²f"(0)/2!]+[x³f⁽³⁾(0)/3!]+....+[x^kf^(k)(0)/k!]

I hope that helps...and I hope that my answer also suggests that you should also attend to your English grammar when asking a question.