) A catenary is described by y=a \cosh \left(\frac{x-x_{0}}{a}\right) where constants a and xo are determined by the position of the end points (x1, Yı) and(x2, Y2). Let us choose

xo = 0 and a = 1 such that y=\cosh x where x and y are dimensionless variables. (a) Using series expansion show that \cosh x=1+\frac{x^{2}}{2}+\ldots (b) The parabola y=1+\frac{{x}^{2}}{2} is an approximation for the catenary. Plot the above parabola and a catenary in the same plot for –1< x < 1 and estimate the maximum error in the approximation.