# Math Help - Taylors approximation problem

1. ## Taylors approximation problem

dx/dt = 1- sin[ ln(1+x )]

Replace the right hand side by the linear Taylor's approximation about x0=0 and solve the resulting equation. Determine the particular solution for the initial condition x(0)=0.

2. Taylor series for $\ln(1+x)$ and $\sin x$

$\ln (1+x) = x - \dfrac{x^2}{2} + \dfrac{x^3}{3} \cdots$
$\sin x = x - \dfrac{x^3}{3!} + \dfrac{x^5}{5!} \cdots$

so to first order the taylor series would be

$\sin (\ln(1+x)) = x$

3. Hadn't learnt the Taylor series so had to do a quick crash course, this helped a lot, thanks heaps.