b. Use Maple to differentiate
and ``simplify'' the result. You got back , although g is different from the answer you got in a. Explain why.
Are all the solutions acceptable? Use a monotonicity argument to show that the above equations cannot have more than one solution.
(The above function is called the ``hyperbolic tangent'' and it is usually denoted by . Its inverse is usually denoted by or )
a. Determine the position of the person when the weight is at a point . Determine the slope of the taut rope.
b. Find the equation of the path along which the weight moves by integrating the above slope.
c. Show that x=0 is a vertical asymptote for the path of the weight. (This means that the weight will never touch the y-axis!).