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

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Homework Help Overview

The discussion revolves around evaluating the limit as x approaches 0 from the positive side for the expression 1/sqrt(x) - 1/sqrt(x^2 + x). The subject area involves limits and the behavior of functions involving square roots.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss manipulating the expression to simplify it, with one participant expressing difficulty in removing x from the denominator. Others present their attempts at algebraic manipulation and question the correctness of their steps.

Discussion Status

Some participants have provided guidance on the limit's behavior, noting the importance of approaching from the positive side due to the domain of the radicals. There is an acknowledgment of the indeterminate form encountered during the limit evaluation.

Contextual Notes

One participant points out a distinction between an expression and an equation, indicating a potential misunderstanding in the formulation of the problem. The discussion reflects varying levels of confidence in the algebraic manipulations performed.

dlp211
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Homework Statement



lim x->0+ 1/x1/2 - 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.
 
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I have manipulated the equation to:

x1/2(x+1) - (x2+x)1/2 / x(x+1)
 
Which I now was able to reduce to:

x(x1/2-x) / x(x+1)

which goes to:

(x1/2-x) / (x+1)

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

Anyone want to check the work I would greatly appreciate it.
 
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
 
Last edited:
dlp211 said:
I have manipulated the equation to:

x1/2(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 =.
 

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