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


Navigation.


Erik Max Francis
 TOP
Welcome to my homepage.


Reference
 UP
A technical reference.


Mathematics reference
 UP
A mathematics reference for students and teachers.


Mathematics reference: Hyperbolic trigonometry identities
 PREVIOUS
Various identities essential in hyperbolic trigonometry.


Mathematics reference: Rules for differentiation
 NEXT
Essential rules for differentiation.


Quick links.


Contents of Erik Max Francis' homepages
 CONTENTS
Everything in my homepages.


Feedback
 FEEDBACK
How to send feedback on these pages to the author.


About Erik Max Francis
 PERSONAL
Information about me.


Copyright
 COPYRIGHT
Copyright information regarding these pages.



Copyright © 2023 Erik Max Francis. All rights reserved.


