Introduction to Limits/Problems

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[edit] An Informal Definition

Find the limit as x approaches 10 for the following statements by finding their values at 9, 9.9, 9.99, 10.01, 10.1, and 11. What values do they surround?

  1. x2
  2. 1 / x
  3. x3 + 4x + 15
  4. (10 − x) / (10 − x)

[edit] Basic Theorems for Limit Operations

  1. Find the limit of f(x)+g(x) and f(x)/g(x) as x approaches 10 with the following functions
    • f(x) =x^2,\,\ g(x) =\sin x
    • f(x) =x^3-4x^2+13,\,\ g(x) =\log(x)
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