1. ## Showing limits

can anyone helpme out with this? gahh...soo hard!

i have to show that lim (1/(x^2 + 1) )= 1 as x --> 0

using limit's definition!
and now i did

|f(x) - L | = | 1/(x^2 + 1) - 1|
| x - 0 | < delta

what does one do from here? im soo stuck

thanks!!

2. Originally Posted by matlabnoob
i have to show that lim (1/(x^2 + 1) )= 1 as x --> 0
using limit's definition!
Try $\displaystyle 1 > \varepsilon > 0\quad \Rightarrow \quad \delta < \sqrt {\frac{\varepsilon }{{1 - \varepsilon }}}$

3. thank you!

but how does that show the limit tends to 1? ........ im confused with it

4. Originally Posted by matlabnoob
thank you!

but how does that show the limit tends to 1? ........ im confused with it
You must show that if $\displaystyle \left| {x - 0} \right| < \delta$ then $\displaystyle \left| {1 - \frac{1}{{1 + x^2 }}} \right| < \varepsilon$.

Now if you expect to have it done for you then you out of luck with me.

5. Originally Posted by Plato
You must show that if $\displaystyle \left| {x - 0} \right| < \delta$ then $\displaystyle \left| {1 - \frac{1}{{1 + x^2 }}} \right| < \varepsilon$.

Now if you expect to have it done for you then you out of luck with me.
i knew this.thanks anyway
ill attempt again