Lecture Notes: Monday, September 14, 1998

 

Limits and One-sided Limits

  1. x^2 as x -> 0.
  2. sin(1/x) as x -> 0.
  3. y = x, x not 0, y = 1 for x = 0 as x -> 0.
  4. 1/x as x -> 0
  5. limit of arctan(x) as x goes to +infinity and -infinity
  6. more on one-sided limits
  7. precise definition of limit

indeterminate forms:

  1. (x^2 - 9)/(x-3) as x -> 0.
  2. sin(4*x)/3*x as x -> 0. Use MAPLE Demo #1 to help.
  3. sqrt(x+1) - sqrt(x) as x -> plus infinity. Rationalize. Also use Demo #1.
  4. (3*x^2 + 2*x - 1)/(x^2 - 8*x) as x -> plus infinity. Calculate, use Demo #1, plot