Graph the curvature function for and find the limit of the curvature as .

Question

Graph the curvature function  for  and find the limit of the curvature as  .

Quizplus · Accepted Answer

Since the curvature function measures the amount of bending in a curve, it makes sense that a continuously straight line would have a curvature of 0. As x approaches infinity, the curve approaches a straight line, meaning the curvature approaches 0. Looking at the choices, option C has a limit of 0 at infinity for the curvature function, so it is the best choice. Option A has a constant non-zero curvature, while options B and D have curves that become steeper and steeper, meaning the curvature does not approach 0 at infinity.

Graph the Curvature Function for and Find the Limit