Mathematics reference
Limits


Properties of limits.


Legend.

 lim_{x > 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.


lim_{x > c} a = a

equation 1


lim_{x > c} x = c

equation 2


lim_{x > c} x^{n} = c^{n}

equation 3


lim_{x > c} (a u) = a lim_{x > c} u

equation 4


lim_{x > c} (u + v) = lim_{x > c} u + lim_{x > c} v

equation 5


lim_{x > c} (u v) = (lim_{x > c} u) (lim_{x > c} v)

equation 6


lim_{x > c} (u/v) = lim_{x > c} u/lim_{x > c} v, lim_{x > c} v != 0

equation 7


lim_{x > c} (u^{n}) = (lim_{x > c} u)^{n}

equation 8


Trigonometry.


lim_{x > c} sin x = sin c

equation 9


lim_{x > c} cos x = cos c

equation 10


lim_{x > c} tan x = tan c

equation 11


lim_{x > c} cot x = cot c

equation 12


lim_{x > c} sec x = sec c

equation 13


lim_{x > c} csc x = csc c

equation 14


Special limits.


lim_{x > 0} (sin x/x) = 1

equation 15


lim_{x > 0} [(1  cos x)/x] = 0

equation 16


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