It seems that I'm a little bit lost about this exercise. It says: Find the taylors polynomial of third degree centered at the origin for $\displaystyle z=\cos y \sin x$. Estimate the error for: $\displaystyle \Delta x=-0.15,\Delta y=0.2$.

So, I did the first part (the easy one), the taylors polynomial for z at (0,0) looks like this:

$\displaystyle f(x,y)=x+\displaystyle\frac{1}{3!}(-x^3+3xy^2)+R_4((x,y),(0,0))$

Then I've found the expression for the error:

$\displaystyle R_4=\displaystyle\frac{1}{4!}(\cos c_2 \sin c_1 x^4+4\sin c_2 \cos c_1 x^3y+6\cos c_2 \sin c_1 x^2y^2+4\sin c_2 \cos c_1 xy^3-\cos c_2 \sin c_1 y^4)$

Now, how do I estimate the error? I have to say that the error will be something like $\displaystyle R_4\leq{}k$, I have to find "k". Should I consider $\displaystyle c_1=0.15, c_2=0.2$? How do I proceed from there?

Bye and thanks for posting!