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Q: Pre-Calculus / Calculus Problem - Evaluating a Limit ( No Answer,   2 Comments )
Subject: Pre-Calculus / Calculus Problem - Evaluating a Limit
Category: Science > Math
Asked by: tamkins-ga
List Price: $10.00
Posted: 18 May 2006 12:29 PDT
Expires: 18 May 2006 13:07 PDT
Question ID: 730146
Please describe (specifically) how to solve the problem posted here:

In other words, I want the steps to solve this problem:
find the limit, as h approaches 0, of

(sqrt(1 + 2(x+h)) - sqrt(1 + 2x)) / h

I know the correct answer, so what I am looking for is the actual
steps taken to get there - the algebra needed to make the formula
above (or posted much more neatly at the link above) solvable when h =

Just to be clear, I do not want just the answer, nor do I want an
alternative-math way of solving this (for instance, by using the chain
rule to attain the derivative of sqrt(1 + 2x)) - what I'm trying to
learn is the underlying technique needed to solve this type of
There is no answer at this time.

Subject: Re: Pre-Calculus / Calculus Problem - Evaluating a Limit
From: kingal-ga on 18 May 2006 12:58 PDT
Hint: Multiply both the numerator and denominator by [sqrt(1 + 2(x+h)
) + sqrt(1+2x) ].
Subject: Re: Pre-Calculus / Calculus Problem - Evaluating a Limit
From: tamkins-ga on 18 May 2006 13:07 PDT
Thank you!  this works :-)

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