How to Multiply by a Conjugate with Multiple Terms?

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Homework Help Overview

The discussion revolves around a limit problem involving the multiplication by a conjugate in the context of two variables and three terms in the numerator. The original poster expresses uncertainty about how to apply this technique in such a scenario.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the method of multiplying by a conjugate, particularly when faced with multiple terms. There are questions regarding the simplification of the limit expression and the interpretation of the original poster's approach.

Discussion Status

The discussion includes attempts to clarify the application of the conjugate method and interpretations of the limit expression. Some participants provide insights into simplifying the expression, while others express confusion about the calculations presented.

Contextual Notes

Participants are navigating the complexities of limits involving multiple terms and are questioning the assumptions made in the original problem setup. There is a focus on understanding the manipulation of expressions rather than arriving at a solution.

dimpledur
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multiplying by a conjugate??

Homework Statement



I am dealing with a limit, however, I am not sure how to multiply by a conjugate when there are two variables and three terms on top. For example

lim [3h + sqrt( 2x +2h) - sqrt( 2x)] / h
h->0


i don't need help solving it, i just need to know how would we multiply it by a conjugate when there are more than 2 terms?
 
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I don't know how you got that but lim h->0 3h/h=3. There. Now you only have two terms in the numerator.
 


how did you get h=3?, I tried the problem as well and got stuck.
 


cam875 said:
how did you get h=3?, I tried the problem as well and got stuck.

I didn't get h=3. I got limit h->0 3h/h=3. That leaves you with figuring out limit h->0 (sqrt(2x+2h)-sqrt(2x))/h.
 

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