I am having trouble proving the limits of quadratic functions such as the following. (I used "E" to represent epsilon and "d" for delta)(adsbygoogle = window.adsbygoogle || []).push({});

lim [(x^2)+1]

x->1

I found the limit, L, to equal 2 and have proceeded through the following steps:

|f(x) - L| < E

| [(x^2)+1] - 1| < E

|[(x^2)-1]| < E

|x+1||x-1| < E

While I also know that 0 < |x-1| < d.

My question is how do you find the numerical relationship between|x+1||x-1|and|x-1|so that I may finddin terms ofE?

(I was thinking of finding the bounded open interval in which |x+1||x-1| = |[(x^2)-1]| and substituting the greastest figure of the interval, which would be greater than |x+1|, in place of |x+1| so that I would have z|x-1|< E where z is an identified numerical value. However, in problems like the one above, |x+1||x-1| = |[(x^2)-1]| within a seemingly unbounded interval.)

please help. your time and assistance is very much appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help with proving limits using Epsilon-Delta definition

**Physics Forums | Science Articles, Homework Help, Discussion**