Math Is Fun Forum

kwinrow

Member

Registered: 2008-07-30

Posts: 11

stuck on this cal 1 problem

prove the statment using the epilson, delta defintion of limit:

lim     x^2+x-6/x-2=5
x→ 2

how do i go about solving this?

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: stuck on this cal 1 problem

you have two choices ,
1. factor it as  x^2+x-6=(x+3)(x-2) , then it would be x+3 =5
2. apply L'hosp...(spelling XD) rule, take derivative 2x+1=5

Last edited by Dragonshade (2008-09-16 06:10:14)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: stuck on this cal 1 problem

I think you misunderstand the problem Dragonshade.  kwinrow must prove the limit by epsilon-delta definition.  Follow Dragonshade's advice about simplifying, but not that this simplification is only valid for x not equal to 2.  Now prove the corresponding epsilon-delta definition, remembering that the definition does not allow x = 2.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: stuck on this cal 1 problem

Oh, my bad

so its there's a relationship e(p) , whenever |x-2|< p ,  | x^2+x-6/x-2  - 5| <e

| x^2+x-6/x-2  - 5| = | (x-2)^2/(x-2)| =|x-2|<e
Then e=p

Last edited by Dragonshade (2008-09-17 04:39:05)