The discussion revolves around evaluating the limit of the hyperbolic tangent function, tanh x, as x approaches infinity. Participants are exploring the mathematical properties and behaviors of the function using its definitions in terms of sinh and cosh.
The discussion includes various approaches to the limit, with some participants providing different methods for simplification. There is no explicit consensus on the final outcome, but several lines of reasoning are being explored.
Some participants question the appropriateness of methods used, such as l'Hospital's rule, while others propose alternative algebraic manipulations. The nature of the problem suggests a focus on understanding the behavior of the function as x increases without bound.
merced said:\lim_{x\rightarrow\infty} tanh x = \lim_{x\rightarrow\infty} \frac{sinh x}{cosh x}
= \lim_{x\rightarrow\infty} \frac{e^x - e^{-x}}{e^x + e^{-x}}
= \lim_{x\rightarrow\infty} \frac{e^{2x} -1}{e^{2x} +1}
what now?