Question

please help me expand the equation using taylor formula

f(x)= tan x up to term x^3

Answer 1

Do you know how to apply Taylor's Theorem?

Answer 2

no

Answer 3

\[f(x)=f(a)+(x-a)f'(a)+\frac{(x-a)^2}{2}f''(a)+\frac{(x-a)^3}{6}f'''(a)\\
\]
use a=pi/4 for simplicity
and find the three derivatives, subtitute for 'a' and expand

Answer 4

\[f(x)=\tan(x)\\
f'(x)=\sec^2(x)\\
f''(x)=2\tan(x)\sec^2(x)
\]
and so on