Consider the surface given bye^x=1+²+². Since we can solve for, aparametrization for is the smooth map:²³

:=R²R³given by(,)=( ln(1+²+²), ,). Compute the tangent vectors_u and_v. Write down the expression for the normal vector field (,)=_u(,)_v(,), and compute(0,1) to find a normal vector to at the point=(0,1)=(ln(2),0,1). Use this normal vector to find the cartesian equation for the tangent plane to at the point. Sketch the surface. splits³into two regions, one of them containing the positive-axis. Let's refer to this region containing the positive-axis as the interior of. Based on the normal vector(0,1) that you computed, would you say that the associated orientation ofis inward or outward? Indicate this orientation on your sketch of

by drawing some sample normal vectors in the direction of.