question says to find the linear approximation of the given mapping at the indicated point

$\displaystyle f(x,y) = (xe^y + cos(y), x, x+e^y); (1,0) $

is this related to the tangent plane to a graph

just take it and use it in this formula

$\displaystyle z = f(x_{0}, y_{0}) + \frac{\partial f}{\partial x}(x_{0},y_{0})(x-x_{0}) + \frac{\partial f}{\partial y}(x_{0},y_{0})(y-y_{0})$