Let be the surface given by the cartesian equation e^x= 1 + y² + z². We can think of S as the graph of the function

f(y, z) = ln(1 + y² + z²).

a) The vector() in this case represents the direction in the -plane for which the corresponding path on the surface at the point sees the largest increase in the-direction. Sketch the surface, mark the point=( ln(2), 0, 1 ), draw the path on in the direction of(), and compute the slope of this path (in the-direction).

b) Now, let's think of S as the zero set of the function g(x, y, z)= e^x - 1 -y² -z². A normal vector to at the point is given by(). Use this to find the cartesian equation for the tangent plane toat the point =( ln(2), 0, 1 )