# Linear approximation of $3$ variable function and its maximum error?

I've got a problem which asks me to find linear approximation of multi-variable function and its maximum error.

Here's the problem :

$$g(x,y,z)=x+x\cos(z)-y\sin(z)+y$$ change if the point $$P(x, y, z)$$ moves from $$(2, -1, 0)$$ a distance of $$ds = 0.2$$ unit toward the point $$(0, 1, 2)$$? Also find an upper bound for the error of it.
I know I should find its linearization $$L(x,y)$$ at $$(2, -1, 0)$$ and plug its $$x$$-increment and $$y$$-increment in $$L(x,y)$$.