Here's the question you clicked on:
jamiemm
fine the limit if it exists: lim of x->0 [[1/(3+x)] - (1/3)]/x
-(1/9) is what I got taking the derivative to the top and bottom after some algebra..
it is -1/9 http://www.wolframalpha.com/input/?i=lim+of+x-%3E0+ [[1%2F%283%2Bx%29]+-+%281%2F3%29]%2Fx And click "show steps"
this is the derivative of \[f(x)=\frac{1}{x}\] at x = 3 but we can do it without the derivative, just with some algebra
hhmmmm. the link gets broken. you'll need to copy/paste it .
\[\frac{1}{3+x}-\frac{1}{3}=\frac{3-(3+x)}{x(3+x)}\] \[=\frac{-x}{3(3+x)}\] divide by x get \[\frac{-1}{3(3+x)}\] replace x by 0 get \[-\frac{1}{9}\]