14. Hyperbolic functions are analogues to trigonometric functions, defined with respect to the unit hyperbola instead of the unit circle. They are particularly useful in the study of differential equations. They can also be defined in terms of exponential functions. One example is the hyperbolic cotangent function coth(x) = etex ex - e-x' defined on the restricted domain x * 0. (a) [3 marks] Find all horizontal asymptotes of coth(x). Answer: (b) [2 marks] Find all vertical asymptotes of coth(x). Answer:(c) [4 marks] Determine where coth(z) is increasing and where it is decreasing, (d) [3 marks] Draw a large sketch of the graph of coth(x) on the axes below, using the information determined in the previous parts of this