Let y be given implicitly as a function of x by the equation: ln(y + x) = y

1. Show that the point (e 1, 1) lies on y(x) defined implicitly by the above equation.

2. Find expressions for dy/dx and d 2y/dx2 .

3. Find the equation of the line that is tangent to y(x) at the point (e 1, 1).