MATH137 Study Guide - Midterm Guide: Intermediate Value Theorem

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

Document Summary

Note: our test only covers up to section 3. 2, while this test covered up section 3. 4. 1. (a) state the precise mathematical de nition of lim x f (x) = . (b) if b(h) is the barometric pressure in kilopascals at height h in kilometers. 2x x2 + 1 (a) lim x 2 (b) lim x 0 (c) lim x 0 (cid:20) sin(3x) x. 3x2: find the derivative of the following functions. (a) f (x) = x ln x (b) g(x) = (cid:112) 1 sin2 x sec(x2 + x) (c) h(x) = 3e2x + 1 (cid:1) = 0: find all x such that sin(cid:0)2x , sketch the graph of y = 2 cos(cid:0)x + (cid:1). 2: find the exact value of cos(sin 1( 1. 2 cos( x) ex + 1: let f (x) = if x < 1 if 1 x 1 if x > 1 x2 + 1)