The hyperbolic sine and cosine are differentiable and satisfythe conditions cosh 0 = 1

Chapter 10, Problem 36

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The hyperbolic sine and cosine are differentiable and satisfythe conditions cosh 0 = 1 and sinh 0 = 0, andddx(cosh x) = sinh x ddx(sinh x) = cosh x.(a) Using only this information, find the Taylor approximationof degree n = 8 about x = 0 for f(x) =cosh x.(b) Estimate the value of cosh 1.(c) Use the result from part (a) to find a Taylor polynomialapproximation of degree n = 7 about x = 0for g(x) = sinh x.

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