Limit as x -> 0 for ((√1+x)-1)/x

Jeann25 · Oct 12, 2005

I need to find the limit as x-> 0 for ((√1+x)-1)/x
but I can't figure out how to get rid of x in the denominator or atleast make the limit not equal to 0 in the denominator. I know this is probably going back some, but it's been a little while since I've done this. I've tried about every trick I can think of, but I can't seem to figure it out, but my book seems to think there's an answer.

Tide · Oct 12, 2005

Are you familiar with l'Hopital's rule?

HallsofIvy · Oct 12, 2005

Tide, L'Hopital's rule is "overkill"!

Jeann25, multiply both numerator and denominator by sqrt(1+x)+ 1 to rationalize the numerator.

Jeann25 · Oct 13, 2005

Thank you for the help!

Tide · Oct 14, 2005

HallsofIvy said:

Tide, L'Hopital's rule is "overkill"!
Jeann25, multiply both numerator and denominator by sqrt(1+x)+ 1 to rationalize the numerator.

Halls,

Of course! But I was trying to ascertain whether the assignment related to a lesson on l'Hospital. :)

Limit as x -> 0 for ((√1+x)-1)/x

Related to Limit as x -> 0 for ((√1+x)-1)/x

1. What is the limit as x approaches 0 for ((√1+x)-1)/x?

2. How can I find the limit as x approaches 0 for ((√1+x)-1)/x?

3. Why is the limit as x approaches 0 for ((√1+x)-1)/x equal to 1/2?

4. Can I use the limit as x approaches 0 for ((√1+x)-1)/x to prove other limits?

5. How does the value of the limit as x approaches 0 for ((√1+x)-1)/x affect the graph of √x?

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