Prove that the limit does not exist (calculus)
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Prove that the limit does not exist (calculus)

Prove that the limit does not exist (calculus)

[From: ] [author: ] [Date: 11-08-14] [Hit: ]
............
I must have missed this in class.
How do I show that this limit does not exist?

lim(x->2) |x^2-4|/(x-2)

-
|x² - 4| is a piecewise function, defined by where its inside changes signs.

(x + 2)(x - 2) = 0
x = -2, 2

Therefore, it is defined as follows:

|x² - 4| = { x² - 4, for x >= 2
............ { 4 - x², for -2 <= x <= 2
............ { x² - 4, for x < -2

The equal signs don't really matter where they're placed, so long as the function remains continuous.

Therefore, when you take this limit, you'll have to take the right hand limit and left hand limit and see if the pieces match up. You should be able to figure out what to do now.

-
|x^2-4|/(x-2)
=|x-2|/(x-2) * |x+2|
Now,|x-2|/(x-2) is a signum function, which is discontinuous at x=2
1
keywords: that,not,calculus,limit,Prove,exist,does,the,Prove that the limit does not exist (calculus)
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .