MATH137 Study Guide - Final Guide: Riemann Sum, Mean Value Theorem

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: All

Document Summary

1 ln x x x 1: find the derivative of each function, f (x) = xe, g(x) = sec(x sinh x, h(x) = t2 sin t dt (cid:90) x. 2: evaluate the following integrals. (cid:90) 2 (cid:90) 2 (cid:90) 1: show that tanh 1 x = (cid:19) (cid:18) 1 + x. 2 ln for |x| < 1: find the area of the region enclosed by y = x2, y = 4x, and y = 2, two men start moving from the same point. One travels south at 6 km/h and the other travels west at 2 km/h. At what rate is the distance between the two men increasing one hour later: let f (x) = sin x. Use the de nition of the derivative to prove that f(cid:48)(x) = cos x: assume that f (x) is di erentiable at x = a and let la(x) denote the linear approxi- mation of f (x) at x = a.