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#math
<delta> verbose, "=sqrt(c7/$i$28)"
<verbose> aaah, thank you
<verbose> forgot that part :)
<GuySoft> mankind_tweezer, i didnt understan this algebric trick you just did now
<mankind_tweezer> OK, which bit doesn't make sense?
<GuySoft> how did you get the 1/x out of the sqrt?
<mankind_tweezer> You mean how did I get it _in_ the sqrt, right?
<GuySoft> mankind_tweezer, ah. thats a diffren aproch.. wait
<GuySoft> ok i got that
<mankind_tweezer> You want to avoid having to differentiate the square-root operation, so instead, put everything under the square-root, calculate the limit of what's under the square-root, and THEN take the square-root of it.
<GuySoft> lets try and get the lim now
<delta> :)
<GuySoft> wait, i got now sqrt(1+ (sin^2(x)/x^2) / x^2
<GuySoft> ..what next?
<mankind_tweezer> I think you made a mistake: the denominator "x^2" should not be there. It should be simply Sqrt[1 + Sin[x]^2 / x^2].
<GuySoft> ah right
<mankind_tweezer> OK. Now, take the limit as x-->0 of what sits inside the square root.
<GuySoft> ok ok.. sinx/x
<GuySoft> if its posative then its 1 and if its negative... ???
<mankind_tweezer> Well, that's 1 from either side.
<mankind_tweezer> The place where the sign of x enters is earlier.
<GuySoft> its sqrt(2) on both sides.. how did we reach that??
<GuySoft> mankind_tweezer, where?
<mankind_tweezer> When you combined everything under the square root, you used implicitly the statement that x is positive.
<mankind_tweezer> Because you wrote Sqrt[x^2] = x.
<GuySoft> ah i see.
<mankind_tweezer> When x is negative, there will be an extra minus sign, Sqrt[x^2] = -x. (Or you could write Sqrt[x^2] = Abs[x] for all x.)
<GuySoft> but how on earth am i supose to discover that..
<mankind_tweezer> So when it's all finished, you should have Sqrt[2] from the positive side and -Sqrt[2] from the negative side.
<GuySoft> mankind_tweezer, i see..
<GuySoft> that was a trick question..
<mankind_tweezer> I really don't know a simpler way of solving this problem! You could more or less discover this sign issue by plugging in a few small values for x, as checks...
<GuySoft> even mbot fell for it
<delta> heh
<GuySoft> we had that on the test a week ago.
<mankind_tweezer> You know, I'm a little surprised by that actually. Mathematica is usually careful about that kind of thing.
<mankind_tweezer> It usually annoys the heck out of you by not even assuming that the variables are _real_, let alone positive.
<GuySoft> well.. "hello bug-report"
<GuySoft> just in time.. i gtg
<mankind_tweezer> Pretty subtle for a test question -- HS or college?
<GuySoft> the open university in israel.. infi 1 course
<GuySoft> 10 point question
<mankind_tweezer> Ah, for university-level it's not so bad, I guess.
<GuySoft> and it said "prove or dis-prove".. so you didnt even know
<delta> % Assuming[x < 0, Limit[(Sqrt[x^2 + Sin[x]^2]) / x, x -> 0]]
<mbot> delta: 1
<delta> Yes!
<mankind_tweezer> How strange!
<GuySoft> delta, that robot would have faild the test..
<delta> ;)
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