Homonym: e^x - e^{-x (Sine)
The expression e^x - e^-x is a mathematical function that combines two exponential functions. Here, e is the base of natural logarithms, approximately equal to 2.718. The term e^x grows rapidly as x increases, while e^-x decreases as x increases. This combination results in a function that is odd, meaning it is symmetric about the origin.
This expression is closely related to the hyperbolic sine function, denoted as \sinh(x) . Specifically, \sinh(x) = \frace^x - e^{-x}2 . The hyperbolic sine function is used in various fields, including mathematics, physics, and engineering, to model phenomena such as waveforms and growth processes.