Find the following limit
Favorites|Homepage
Subscriptions | sitemap
HOME > > Find the following limit

Find the following limit

[From: ] [author: ] [Date: 12-08-27] [Hit: ]
......
Lim as x approaches infinity square root of 4x^2 + 1/ (x-1)

The sq root is only over the 4x^2 + 1

-
√(4x^2 + 1) / (x-1)

divide everything by x.

√(4x^2 + 1)/x / (x-1)/x

√(4x^2/x^2 + 1/x^2) / (x/x - 1/x)

√(4 + 1/x^2) / (1 - 1/x)

as x--> ∞

√(4 + 0) / (1 - 0)

√4/1

2/1 = 2

-
Use L'Hopital's rule
Derivative of numerator = 4x/(4x^2+1)^(1/2)
Derivative of denominator = 1
lim x-> inf 4x/(4x^2+1)^(1/2) = 4x/2x = 2

-
At the limit, we can forget about the +1, so we get lim (x -> inf) sqrt 4x^2 / (x - 1) = lim (x -> inf) 2x / (x - 1), which is 2.

-
The answer is 2.
1
keywords: limit,the,following,Find,Find the following limit
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .