find limit, as x goes to 0, of (1/x*sqrt(1+x)) - (1/X)

[fisch512]

I've been stuck on this problem for a while now and I could use a hint or two on where to go next.

The problem is: Limit[sub:25th18fa]as x approaches 0[/sub:25th18fa] ((1/x*sqrt(1+x)) - (1/X))

I simplified it to (1 - sqrt(1+x)) / (x * sqrt(1+x))

This is where I got stuck and I could use some help on what the next step is.

 

[mmm4444bot]

One method ...

Hello Fisch:

Your simplification is a good start.

Now, you've got a situation where there is a factor of x in the denominator that prevents you from simply substituting 0 for x to calculate the limit.

You can fix that situation after multiplying by [1 + sqrt(x + 1)]/[1 + sqrt(x + 1)].

If you need more help, then please post your work so far and explain why you're stuck.

Cheers,

~ Mark