- #1
honestrosewater
Gold Member
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- 6
Problem
Find the limit.
[tex]
\lim_{x \rightarrow 0} \frac{\frac{1}{x + 1} - 1}{x}
[/tex]
My attempt
I'm totally stuck. domain(f) = R - {0}. Setting g: R - {-1} --> R, g(x) = 1/(x+1) - 1 and h: R --> R, h(x) = x, g and h are both continuous, but g(0) = 0 and h(0) = 0. It looks like f(0) is just a hole. Perhaps I will try factoring again. My book says the limit is -1, but I don't see how it expects me to find it.
Find the limit.
[tex]
\lim_{x \rightarrow 0} \frac{\frac{1}{x + 1} - 1}{x}
[/tex]
My attempt
I'm totally stuck. domain(f) = R - {0}. Setting g: R - {-1} --> R, g(x) = 1/(x+1) - 1 and h: R --> R, h(x) = x, g and h are both continuous, but g(0) = 0 and h(0) = 0. It looks like f(0) is just a hole. Perhaps I will try factoring again. My book says the limit is -1, but I don't see how it expects me to find it.