The hyperbolic cosine of x, denoted by cosh x, is defined by

This function occurs often in physics and probability theory. The graph of y = cosh x is called a catenary.

(a) Use differentiation and the definition of a Taylor series to compute the first four nonzero terms in the Taylor series of cosh x at x = 0.

(b) Use the known Taylor series for ex to obtain the Taylor series for cosh x at x = 0.

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cosh x = (e+e).