MATH137 Midterm: MATH137 Midterm 1 2014 Fall Solutions

• 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 sin(3x) x (cid:4) (c) lim x 0. 3x2: find the derivative of the following functions. (a) f (x) = x ln x (b) g(x) = (c) h(x) = (cid:8) 3e2x + 1: find all x such that sin (cid:2) (cid:3) 2: sketch the graph of y = 2 cos, find the exact value of cos(sin. 2 cos( x) ex + 1: let f (x) = if x < 1 if 1 x 1 if x > 1. 1 x, then f (cid:4) (x) = 1 x2+1 . (b) show that if f (x) = sinh (cid:13) x2 + 2x 1.