MATH 120 Midterm: MATH 120 2012 Winter Test 1
Document Summary
Be sure that this examination has 12 pages including this cover. Evaluate the following limits. (a) lim x (ln x)2e x (b) (c) (d) lim x 1 x2 ln(1 + x) x (cid:2) x2 + 5x x sin2 (cid:0) 1 x(cid:1) lim x lim x 0. The quantities p, q and r are functions of time and are related by the equation r = p q. Assume that p is increasing instantaneously at the rate of 8% per year and that q is decreasing instantaneously at the rate of 2% per year. Determine the percentage rate of change for r. Use the formal de nition of limit to prove that lim x 0 cos(3 sin x) = 1. The hyperbolic trigonometric functions sinh(x) and cosh(x) are de ned by sinh(x) = ex. They have many properties that are similar to corresponding properties of sin(x) and cos(x).
