## jamiemm Group Title fine the limit if it exists: lim of x->0 [[1/(3+x)] - (1/3)]/x 3 years ago 3 years ago

1. 101Ryan101 Group Title

-(1/9) is what I got taking the derivative to the top and bottom after some algebra..

2. 101Ryan101 Group Title

anyone else?

3. satellite73 Group Title

that is right

4. fiddlearound Group Title

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"

5. satellite73 Group Title

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

6. fiddlearound Group Title

hhmmmm. the link gets broken. you'll need to copy/paste it .

7. satellite73 Group Title

$\frac{1}{3+x}-\frac{1}{3}=\frac{3-(3+x)}{x(3+x)}$ $=\frac{-x}{3(3+x)}$ divide by x get $\frac{-1}{3(3+x)}$ replace x by 0 get $-\frac{1}{9}$