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Algebra of Limits

Let 81927.png = l and 81921.png = m. If l and m exist, then
  1. 81915.png = 81909.png ± 81903.png = l ± m
  2. 81897.png (x) = 81891.png
  3. 81885.png, provided m ≠ 0
  4. 81879.png = k 81872.png, where k is a constant
  5. 81866.png = 81859.png= | l |
  6. 81853.png = 81847.png = lm
  7. If f(x) ≤ g(x) for every x in the deleted nbd of a, then 81841.png
  8. If f(x) ≤ g(x) ≤ h(x) for every x in the deleted nbd of a and 81835.png
     
    This result is often stated as sandwich theorem.
  9. 81829.png = 81823.png
     
    In particular,
    1. 81817.png = 81811.png
    2. 81805.png
  10. If 81799.png = +∞ or – ∞, then 81793.png = 0




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