Question

Limits!
For the given limit, then find the limit L (evaluate it), then use the Epsilon-Delta definition of a limit to prove that the limit is L (prove that whatever you evaluated is correct).
The limit of (x^2+1) as x approaches 1.

Answer 1

oh damn, epsilon delta proofs let see.

Answer 2

I have the answer key, and have gotten to step 6, but whatever occurs in step 7 is beyond me.

Answer 3

limx goes to (x^2 +1)=2. epsiolon delta def says lX-Xol<d(delta) implies lf(x)-Ll<E(epsilon). Plug it in so lx-1l<d implies lx^2-1l<E, lx+1llx-1l<E, stipulate d<1(smaller than or equal to 1), lx-1l<1, so -1<x-1<1 , 1<x+1<3, so if lx+1llx-1l<E than 3lx-1l<E, so 3d=E, d=E/3. so d=min{1,E/3}. you now need to validate that this is true which I leave to you.

Answer 4

well they just use the fact that if you let d< or equal to 1, than lx-1l<1 and by rearranging as i have done above you get that step. They missed a huge step here but meh books are bad.

Answer 5

the validation is step 10 and on which I left to you. :D enjoy brah and dont forget to become a fan.

Answer 6

Thanks for you help :D

Answer 7

no problemo