Limit help(1/rad(x) - 1/rad(x^2 + x))

[dlp211]

Homework Statement

lim x->0⁺ 1/x^1/2 - 1/(x²+x)^1/2

Homework Equations

inf - inf

The Attempt at a Solution

I can't get x out of the bottom of the equation.

 

[dlp211]

I have manipulated the equation to:

x^1/2(x+1) - (x²+x)^1/2 / x(x+1)

 

[dlp211]

Which I now was able to reduce to:

x(x^1/2-x) / x(x+1)

which goes to:

(x^1/2-x) / (x+1)

and so my limit is 0/1 which is zero.

Anyone want to check the work I would greatly appreciate it.

 

[QuarkCharmer]

Yeah, that limit is tending to 0. It's important that it's from the positive side because of the domain of the radicals.

I simply combined the fractions and the limit went to the indeterminate form 0/0. Then I just L'Hopital ruled it into 0/1

 

[Mark44]

I have manipulated the equation to:

x^1/2(x+1) - (x²+x)^1/2 / x(x+1)

This is not an equation - it's an expression. An equation has two expressions that are connect by =.