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1.3 For each positive constant r, the smooth curve given by r a(u) = -(u cosh u - sinh u, 1), cosh u is called a tractrix. Taking r 1, show that, for u > 0, a(u) is the curve traced out by a stone starting at (0,1) on the end of a piece of rope of length 1 when the tractor on the other end of the piece of rope drives along the positive x-axis starting at (0,0). In more mathematical terms, show that a(u) +t(u) is on the positive x-axis for u > 0 (and that a(0) = (0,1)). Sketch the trace of the curve for all real values of u. 13 For each positive constant r, the smooth curve given by r a(u) = (u cosh u sinh u, 1), cosh u is called a tractrix. Taking r = 1, show that, for u > 0, alu) is the curve traced out by a stone starting at (0,1) on the end of a piece of rope of length I when the tractor on the other end of the piece of rope drives along the positive x-axis starting at (0,0). In more mathematical terms, show that a(u) + f(u) is on the positive x-axis for u > 0 (and that a(0) =(0,1)). Sketch the trace of the curve for all real values of u