Consider the curveparametrized by()=(, 1, 12+2²), . You can think ofas the intersection of the paraboloid=²+²

with the plane+=1. Sketch the portion of this curve in the first octant, and computec^'(1/2), which is a vector tangent to at the point

c(1/2)=(1/2, 1/2, 1/2). Use the direction of the tangent vectorc(1/2)to determine the orientation of. Indicate this orientation by drawing arrows along the trace of the curve. Finally, sketch the tangent line toat the pointc(1/2)=(1/2, 1/2, 1/2). What is the parametrization()for this tangent line?