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

1. 101Ryan101

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

2. 101Ryan101

anyone else?

3. satellite73

that is right

4. fiddlearound

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

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

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

7. satellite73

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