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Important Expansions

Sometimes, following expansions are useful in evaluating limits. Students are advised to learn these expansions.
  1. loge (1 + x) = x81730.png
  2. loge (1 – x) = –x81724.png
  3. ex = 1 + x + 81718.png
  4. ex = 1 – x + 81712.png
  5. ax = 1 + x (loge a) + 81705.png
  6. sin x = x81699.png
  7. cos x = 1 – 81693.png
  8. tan x = x + 81687.png




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