I searched, but couldnt find any examples.
I am given the following function:
$ f(x,y) =sin(sinx+siny)$
I am required to find the taylor polynomials of order $n=1$ around $ a = (0,0)$, and to express the remainder and to bound it as tight as possible in the domain of $K = \{(x,y) \ s.t. \ |x| + |y| \leq \frac{1}{2}\} $.
After calculating, I found that the taylor polynomial of order n=1 around the given $ a = (0,0)$ is $ Tf (x,y) = x + y $, and after a lot of derivatives I also saw that all the partial derivatives of order $2$ are equal to $0$ at the point $a$.
Thus I have :
$ R_2 f(x,y) = f(x,y) - T_2 f(x,y) = sin(sinx+siny) - (x+y)$
And also:
$ R_2 f(x,y) = \frac{D_{(x,y)} ^3 f(c)}{3!} $ for c between $(0,0),(x,y)$.
The class notes are horrendous and no explanation is given as to how to continue from here. I will appreciate any info, tips, and guidance. Thanks!