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0:00 Introduction. 1:26 (a) Showing that f(x) is even. 2:55 (b) f(x) on |x| ≤ 1. 5:42 (c) f(√2). 9:34 (d) f(x) on |x| > 1. 19:45 (e) Asymptotes of f(x), crude (approximation) method. 23:05 (e) Asymptotes of f(x), rigorous (limit) method. 28:00 Graphical visualization of f(x). 28:22 Bonus problem. A long, multi-step problem where you have to find the alternative expression for function f(x) defined as an integral. The catch is, variable x is located at the awkward spot inside the integral. #integration #calculus #EvenFunction #integral #AbsoluteValue #DefiniteIntegral #asymptotes ------------------------------------------------------------------------- CORNERSTONES OF MATH features quality math problems to strengthen your math fundamentals and problem-solving ability. Problems are generally on high school level (with some deviations), spanning over topics such as algebra, discrete mathematics, calculus, geometry, statistics, trigonometry, etc. I hope that this channel provides some intellectual pleasure and make you appreciate the beauty of math itself. Please consider giving a Like to this video and Subscribing to my channel, it really means a lot for the creator like me, and you will be introduced to many more interesting math videos!