Page 1 of 1
Since the hyperbolic functions are defined in terms of exponential functions, it is natural to expect that their inverse
Posted: Thu Jul 14, 2022 4:41 pm
by answerhappygod
- Since The Hyperbolic Functions Are Defined In Terms Of Exponential Functions It Is Natural To Expect That Their Inverse 1 (49.9 KiB) Viewed 45 times
Since the hyperbolic functions are defined in terms of exponential functions, it is natural to expect that their inverses should be defined in terms of logarithms. Indeed this is the case; for example, sinhx=2ex−e−x (i) arcsinhx=log(x+x2+1),x∈R (ii) a. Derive (ii) from (i). b. Use (i) to show that arccschx=arcsinhx1. c. Use part b. and (ii) to carefully show that dxdarccschx=−∣x∣1+x21, making sure to clearly explain where the absolute value comes from.