video1.0<iframe src="https://www.loom.com/embed/45196965f50745f78396911918ed3d02" frameborder="0" width="1838" height="1378" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>13781838Loomhttps://www.loom.com13781838https://cdn.loom.com/sessions/thumbnails/45196965f50745f78396911918ed3d02-bb5e93d5f4a75798.gif2391.329967I work through several hyperbolic functions questions step by step. First, I prove tanh inverse x equals one half ln of 1 plus x over 1 minus x, then use it to solve for x in a later part while rejecting invalid solutions. I then compute a volume of revolution about the y axis using an integral in terms of sinh and exponentials, giving a final numeric form. After that, I determine exact x coordinates of stationary points for a curve, and I finish with a hyperbolic substitution integral and a definite integral with a final expression involving ln and root 2. I did not request any action from viewers.