Posted by T.Gracken on August 04, 2002 at 21:20:44:
In Reply to: Update on T. Gracken's July 26, 2002 at 12:33:57 post (a limit problem) posted by Dr. Andrew Coultos on August 02, 2002 at 13:57:47:
: T. Gracken,
: let me identify four of your lines in your post by
: using I, II, III, and IV. My versions of your lines should be equivalent to yours.
: I: lim(x->0){e^ln[e^x + x]^(2/x)}
: II: lim(x->0){e^[2ln(e^x + x)/x}
: III: lim(x->0){e^[2(e^x + 1)/(e^x + x)]}
: IV: e^4
: point 1) (I) does not lead to (II). If you move the "2" down as a multiplier on the ln expression, then (I) would lead to this:
: lim(x->0){e^[2ln(e^x + x)^(1/x)}.
:
: point 2) You are missing a "]" in line (II). Or you
: should not have had any brackets in this line at all?
:
: point 3) (II) does not lead to (III). If your line (II) had been correct, then your line (III) is wrong
: because it is not the limit of the derivative seen in
: (II). The derivative in line (II) is more complicated
: than what you typed for (III), and it is
: (e^x + x)[2x(e^x + 1)/(e^x + x) - 2ln(e^x + x)].
:
: point 4) Although (IV), the correct answer, does follow from (III), the work of showing what value the limit is, as a whole, is wrong because (III) as already mentioned has come about by a wrong method.
: (If you want, print this off and hold my feet to the fire for any of the particulars of which I discussed.)
I have no problem with you pointing out the typo's I made. I suppose I should quit attempting to write responses using HTML tags for aesthetic purposes to decrease the typical typo's I commonly enter. However, I am still anxious to read your views on the actual question at hand. Not, "can you find Mr.G's typo's and attempt to humiliate him for his typo's?", but "can you provide justification or counter example to other posts on this topic that are in question?"
I'm assuming that you aren't sure (or don't know) since you have not addressed the issue.