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2. Taylor Series: We have seen how, given differentiable functions over a certain interval, power series can be used to represent these functions over their intervals of convergence. Because power series are polynomial series, the coefficients of the terms can be determined via differentiation, which leads to Taylor series. When the series are centered around x = 0, the Taylor series are referred to more specifically as Maclaurin series. Using what you know about the Maclaurin series for f(x) = e", find the Maclaurin series for the basic hyperbolic functions, g(x) = cosh(x) and h(x) = sinh(x) [You will need to look up the definitions of these two functions first]. Do these series have any similarities to other Maclaurin series that you have already seen? Explain what you observe. Finally, using Euler's identity, show very carefully the connections between the hyperbolic functions and the two familiar functions that go with the Maclaurin series you have already seen