Solution Found!
The hyperbolic functions cosh z and sinh z are defined as
Chapter 2, Problem 2.33(choose chapter or problem)
The hyperbolic functions cosh z and sinh z are defined as follows: ez e' cosh z = and sinh z = ez ez 2 2 for any z, real or complex. (a) Sketch the behavior of both functions over a suitable range of real values of z. (b) Show that cosh z = cos(iz). What is the corresponding relation for sinh z? (c) What are the derivatives of cosh z and sinh z? What about their integrals? (d) Show that cosh2 z sinh2 z = 1. (e) Show that f dx 1,\/1 x2 = arcsinh x. [Hint: One way to do this is to make the substitution x = sinh z.]
Questions & Answers
QUESTION:
The hyperbolic functions cosh z and sinh z are defined as follows: ez e' cosh z = and sinh z = ez ez 2 2 for any z, real or complex. (a) Sketch the behavior of both functions over a suitable range of real values of z. (b) Show that cosh z = cos(iz). What is the corresponding relation for sinh z? (c) What are the derivatives of cosh z and sinh z? What about their integrals? (d) Show that cosh2 z sinh2 z = 1. (e) Show that f dx 1,\/1 x2 = arcsinh x. [Hint: One way to do this is to make the substitution x = sinh z.]
ANSWER:Step 1 of 9
a)
The plots for the function
