can someone help me with a quick math 1a problem?

Colleges and Universities A-Z University of California - Berkeley
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<p>i know we're not supposed to get math help on here. but just this once becasue different people are giving me different answers and i have a final tomorrow...</p>

<p>ok lim x->0 of cos(2x)/(sin(x))^2</p>

<p>in case its confusing, the bottom is sin(x) the quantity squared</p>

<p>when i tried it, i got 1/0 which i presumed to mean infinity</p>

<p>but my roommate said 1/0 means the lim DNE because of the denominator</p>

<p>(when i graph it, it goes to infinity from the RH and LH.)</p>

<p>so...when a limit goes to inf, we say it appraches inf
and when it takes the form c/0 where c is pos or neg constant, i am assuming it then goes to plus/minus inf</p>

<p>and just to clarify then, the only time we would say a lim DNE exist is if the LHS lim DN = the RHS?</p>

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<p>wait, you can simplify your limit down to:</p>

<p>lim x-> 0 of cot ^2 (x) - 1
by the double angle formula of Cosine (cos 2x = cos^2 (x) - sin ^2 (s) )</p>

<p>The answer has to be positive infinity, since cot^2 (x) goes to positive infinity at x -> 0</p>

<p>This is really similar to something like 1 / x^2 vs. 1/x. With 1/x, you have to specify which side of zero you are approaching the function from, since it makes a difference. But, for 1/x^2, it doesn't, since both tails go to positive infinity.
What you said is right. The only time a limit is DNE is when left limit =/= right limit</p>

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<p>thank you!!!</p>

<p>but if i hadnt simplified the way you did for my final tomorrow would i be docked points for not using the double angle identities even though i came up with the same answer?</p>

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<p>A limit cannot that approaches infinite DNE. If we say that the limit approaches infinite, we are simply explaining how the limit FAILS to exist.</p>

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<p>Formally, you show the existence of a limit by setting up a delta-epsilon proof. I don't think you can evaluate if infinite minus something is smaller than epsilon, so the proof method won't work. OTOH, I also feel that noting how a fxn behaves at a point can be useful (ie, explodes on both sides to +inf versus a fxn that goes to +inf on one side and -inf from the other side). That's the issue with math classes when the application is so far away; it's not clear what your motivation for the question is.</p>

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<p>I effing hate delta-epsilon. With a passion.</p>

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<p>webhappy and Indian: I AGREE!!!</p>

<p>and delta-epsilon for proving infinite limits makes me want to gauge my eyes out of my head...stpuid M's and N's...i really have no idea what to do with those :(</p>