MATH137 Lecture Notes - Lecture 3: Paula Smith, Classification Of Discontinuities

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Catherine Briggs

Document Summary

Math 137 week 3 notes dr. paula smith: hyperbolic functions, combinations of ex and e-x x sinh x cosh x tanh = x e e. 2 sinh x e x x cosh x x csc hx sec hx coth = x x. Dom sinh(x) = , ran sinh(x) = . Dom cosh(x) = , ran cosh(x) = [1, ) 1 tanh2x = sech2x y = cosh 1 x cosh y = x and y 0 y = tanh 1 x tanh y = x: sinh 1 x = ln(x + Strategy: first we substitute a = 2, f(x) = 3x 7, l = 1 in the de nition. 2| < implies |(3x 7) ( 1)| < . |(3x 7) ( 1)| = |3x 6| = 3|x 2| . If |x 2| < , then 3|x 2| < 3 . This will be less than if 3 .