Question

The hyperbolic cosine and hyperbolic sine functions, f(x) cosh(x) and g(x) sinh(), are analogs of the trigonometric functions cos(x) and sin(z) and come up in many places in mathematics and its applications. (The hyperbolic cosine, for example, describes the curve of a hanging cable, called a catenary.) They are defined by the conditions cosh(0)-l, sinh(O), (cosh())inh("), d(sinh()- csh) (a) Using only this information, find the Taylor polynomial approximation for cosh(x) at0 of COS degree n = 4. (b) Using only this information, find the Taylor polynomial approximation for sinh(x) at0 of degree n 5 (c) Using your work in (b), estimate sinh(1) (d) Here's an alternative approach to (a): Take the derivative of the Taylor polynomial you found in (b). Do this, and compare to your answer in (a).

Answer 1

3 2-1 3 i b) 니 5! SI

120 20 + 120 二 14; /20 1,175 (d) sinh 1 3 3 2 3 I 51 5 t l 2.1