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!