A man initially standing at the point O walks along a pier pulling a rowboat by a rope of length L. The man keeps the rope straight and taut. The path followed by the boat is a curve called a tractrix and it has the property that the rope is always tangent to the curve (see the figure). (a) Show that if the path followed by the boat is the graph of the function y fsxd, then f9sxd dy dx 2sL2 2 x 2 x (b) Determine the function y fsxd.
1.2 Finding limits Graphically To find the limit graphically of a function you have to follow the function from both the positive side and from the negative side of the coordinate system towards the number x approaches. For example, For this function as x approaches -2, if you follow the function from both sides the limit equals 4. 1.3 Finding limits Numerically To find the limit of a function numerically there are different step you have to take: 1. To start finding the limit of a function you have to substitute the number that approaches x in the limit. For example, lim (3 + 2) = 3(-3) + 2 = -7 ▯→▯▯ 2. In the case that the limit is unsolvable by substitution you have to simplify the function by