Find the Maclaurin series for sinh(x) = e*-e*, and cosh(x) = e*+e* 2 2 in two...

 

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Find the Maclaurin series for sinh(x) = e*-e*, and cosh(x) = e*+e* 2 2 in two different ways. These are the hyperbolic sine and hyperbolic cosine functions, respectively. a) Compute the values of sinh(0 )and cosh(0). b) Show that sinh(x) = cosh(x) dx cosh(x) and cosh(x) dx and = sinh(v). c) Find the values of the first 8 derivatives of sinh(x), evaluated at x=0. This should be enough for you to see the pattern to get the values of all the higher derivatives of sinh(x )at x=0. d) Form the Maclaurin series for sinh(x). It should look similar to the Maclaurin series for sin(x). What is the difference, though? e) Repeat (c) and (d) for cosh(x). Find the Maclaurin series for sinh(x) = e*-e*, and cosh(x) = e*+e* 2 2 in two different ways. These are the hyperbolic sine and hyperbolic cosine functions, respectively. a) Compute the values of sinh(0 )and cosh(0). b) Show that sinh(x) = cosh(x) dx cosh(x) and cosh(x) dx and = sinh(v). c) Find the values of the first 8 derivatives of sinh(x), evaluated at x=0. This should be enough for you to see the pattern to get the values of all the higher derivatives of sinh(x )at x=0. d) Form the Maclaurin series for sinh(x). It should look similar to the Maclaurin series for sin(x). What is the difference, though? e) Repeat (c) and (d) for cosh(x).

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a Determine sinh0 and cosh0 values Whereas cosh0 e0 e0 2 1 1 2 1 sinh0 e0 e0 2 1 1 2 0 b Prove that ... View the full answer