(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the limit.

[tex]\lim_{x\rightarrow0}\frac{\frac{1}{x+1}-1}{x}[/tex]

2. Relevant equations

3. The attempt at a solution

I have to do this analytically. Although, I know that the limit is supposed to be -1 from a graphing approach. When you substitute in 0 for x you get 0/0. How do I get this function into a determinate form? I cant factor and I'm not sure what to multiply the top and bottom by.

I tried [tex]\frac{\frac{1}{x+1}+1}{\frac{1}{x+1}+1}[/tex]

and I got

[tex]\frac{1-(x^2+2x+4)}{x(x+1)(x+2)}[/tex] which is still in indeterminate form.

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# Homework Help: Cancellation Limit

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