In Exercises $37 - 42$ , use the partial derivatives of role="math" localid="1650186853142" $g (x, y) = \tan^{- 1} (x y^{2})$ and the point role="math" localid="1650186870407" $(1, 0)$ specified to
$(a)$ find the equation of the line tangent to the surface defined by the function in the $x$ direction,
$(b)$ find the equation of the line tangent to the surface defined by the function in the $y$ direction, and
$(c)$ find the equation of the plane containing the lines you found in parts $(a)$ and $(b)$ .

Question

Accepted Answer

Part $(a)$ , The equation of the line tangent to the surface defined by the function in the $x$ direction is

$x = 1 + t, y = 0, z = 0$

Part $(b)$ , The equation of the line tangent to the surface defined by the function in the $y$ direction is

$x = 1, y = t, z = 0$

Part $(c)$ , The equation of the plane containing the lines you found in parts $(a)$ and $(b)$ is

$z = 0$

Short Answer