The hyperbolic sine of x is defined by

Repeat parts (a) and (b) of Exercise 23 for sinh x.

Exercise 23

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.

Transcribed Image Text:

sinh .x=;(e^ – e ) -