Solving Confusing Limits Homework

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    Confusing Limits
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Homework Help Overview

The discussion revolves around evaluating limits involving square roots, specifically the limits as h approaches 0 and x approaches 1. The participants are exploring methods to simplify these expressions without resorting to L'Hôpital's Rule.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using the conjugate to simplify the expressions. There are attempts to factor and manipulate the limits to find solutions. Questions arise regarding the effectiveness of these methods and the results obtained from them.

Discussion Status

Some participants have shared their results after applying suggested techniques, while others have provided guidance on factoring and using conjugates. There is an acknowledgment of different approaches being explored, but no explicit consensus has been reached.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the methods they can use. There is also a mention of a previous comment that should be disregarded, indicating some uncertainty in the discussion.

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Homework Statement



1. limh->0 (sqrt(a+h)-sqrt(a))/h
2. limx->1 (1-sqrt(x))/(1-x)

Homework Equations



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The Attempt at a Solution



I tried conjugate, etc., but couldn't solve it without L'H's Rule.
 
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Using the conjugate will work. What did you get when you tried that?
 
Thanks I got 1/(2)for one and 1/2 for number 2
 
Last edited:
For the second one, try factoring the numerator like so:

[tex]1 - x =\left(1 - \sqrt{x}\right)\left(1 + \sqrt{x}\right)[/tex]

The solution should then become obvious.

EDIT: And for the first one, multiplying by the conjugate of the numerator is what you need to do.
 
Thanks guys, got them.

Ignore my comment above this.
 

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