Mathematics reference
Limits
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Properties of limits.
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Legend.
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- 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.
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Basic.
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limx -> c a = a
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equation 1
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limx -> c x = c
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equation 2
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limx -> c xn = cn
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equation 3
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limx -> c (a u) = a limx -> c u
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equation 4
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limx -> c (u +- v) = limx -> c u +- limx -> c v
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equation 5
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limx -> c (u v) = (limx -> c u) (limx -> c v)
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equation 6
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limx -> c (u/v) = limx -> c u/limx -> c v, limx -> c v != 0
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equation 7
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limx -> c (un) = (limx -> c u)n
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equation 8
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Trigonometry.
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limx -> c sin x = sin c
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equation 9
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limx -> c cos x = cos c
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equation 10
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limx -> c tan x = tan c
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equation 11
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limx -> c cot x = cot c
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equation 12
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limx -> c sec x = sec c
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equation 13
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limx -> c csc x = csc c
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equation 14
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Special limits.
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limx -> 0 (sin x/x) = 1
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equation 15
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limx -> 0 [(1 - cos x)/x] = 0
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equation 16
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