Question

Limits

Answer 1

\[\lim_{x \rightarrow 0} \frac{\frac{ 1 }{ 3+x } - \frac {1}{3} }{ x}\]

Answer 2

The z was suppose to be an x.

Answer 3

Get a common denominator:
\[\lim_{x \rightarrow 0} \frac{\frac{3-3-x}{3(3+x)}}{x}= \lim_{x \rightarrow 0} \frac{-1}{3(3+x)}=\frac{-1}{9}\]

Answer 4

Check: http://www.wolframalpha.com/input/?i=limit+as+x+goes+to+zero++of+%281%2F%283%2Bx%29+-+1%2F3%29%2F%28x%29