Question

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

Answer 1

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

Answer 2

anyone else?

Answer 3

that is right

Answer 4

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"

Answer 5

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

Answer 6

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

Answer 7

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