GRAPHS OF THE HYPERBOLIC FUNCTIONS The graphs of the hyperbolic functions, which are shown in Figure 6.9.1, can be generated with a graphing utility, but it is worthwhile to observe that the general shape of the graph of y =e y = cosh x y= sinh x tanh x (a) (b) (c) Jeremy EdwardsiStockphoto The design of the Gateway Arch in St. Louis is based on an inverted hyper- bolic cosine curve (Exercise 73). y- coth x y= sech x y esch x (d) (e) (f) A Figure 6.9.1

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.