Mathematics reference
Limits
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Properties of limits.

Legend.
  • limx -> c u means "the limit as x approaches c of u,"
  • a, c, and n are constants,
  • u and v are functions of x.
Basic.
limx -> c a = a equation 1
limx -> c x = c equation 2
limx -> c xn = cn equation 3
limx -> c (a u) = a limx -> c u equation 4
limx -> c (u +- v) = limx -> c u +- limx -> c v equation 5
limx -> c (u v) = (limx -> c u) (limx -> c v) equation 6
limx -> c (u/v) = limx -> c u/limx -> c v, limx -> c v != 0 equation 7
limx -> c (un) = (limx -> c u)n equation 8
Trigonometry.
limx -> c sin x = sin c equation 9
limx -> c cos x = cos c equation 10
limx -> c tan x = tan c equation 11
limx -> c cot x = cot c equation 12
limx -> c sec x = sec c equation 13
limx -> c csc x = csc c equation 14
Special limits.
limx -> 0 (sin x/x) = 1 equation 15
limx -> 0 [(1 - cos x)/x] = 0 equation 16
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