(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use Definition 2.4.1 to prove that the stated limit is correct.

Definition 2.4.1 in my book is:

lim as x->a of f(x) = L

if given any number e(epsilon)>0 we can find a number d(delta)>0 such that

|f(x)-L|<e if 0<|x-a|<d

2. Relevant equations

Question 31. lim as x>-2 of 1/(x+1) = -1

Question 33. lim as x>4 of sqrt(x) = 2

3. The attempt at a solution

31. |1/(x+1) + 1|<e, 0<|x+2|<d

|(x+2)/(x+1)|<e

set d<=1

-1<x+2<1, -2<x+1<0

|x+1|<0

|x+2|< e * |x+1|

...then I get stuck

32. |sqrt(x)-2|<e, 0<x-4<d

sqrt(x)<e-2

x<(e-2)^2

x-4<(e-2)^2-4

...by here I'm probably already wrong

d=(e-2)^2-4

4. The answers in the back of the book

31) d=min(1,e/(1+e))

33) d=2e

P.S. Sorry, I don't know how to use Latex or whatever mathematical typing system you guys use here, so it's a little messy/unreadable.

Thanks in advance for the help!

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# Homework Help: 2 Limit questions

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