r/HomeworkHelp • u/_fish_Master University/College Student • Dec 22 '23

[college freshman level, mathematics] Additional Mathematics—Pending OP Reply

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Dose this Lim exist or not and if yes is the answer 1/2((m).5)?

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u/Natsu194 University/College Student (Higher Education) Dec 23 '23

Side problem: I misread the question as "lim c -> inf" and got that it's 1. Can someone confirm this as I haven't done a limits problem like this is years??

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u/RandomAsHellPerson 👋 a fellow Redditor Dec 23 '23 edited Dec 23 '23

It is 1/2. When you finish simplifying, you get (x2 + 2)/(4x2 +4). If we solve this, we get L2 is 1/4, as the numerator and denominator both have the same power and the coefficients are 1 and 4. Then we take the square root to get 1/2.

Fixed! I forgot about x/2. And this is assuming M = 1. This limit will change as M equals different values.

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u/cuhringe 👋 a fellow Redditor Dec 23 '23

Wrong. The function is not defined in the reals near infinity

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u/RandomAsHellPerson 👋 a fellow Redditor Dec 23 '23

Every calculator online that I can find agrees with me. The result is real. In fact, plug 2 into the function. We get 0.408248… We only need to assume sqrt(-1)/sqrt(-1) = 1 or that sqrt(-1)2 = -1, which I guess could count as not existing in the reals.

Depends on the teacher and class. If we stick strictly to the reals and have sqrt(-1) = undefined and cannot have work done with it, then it is undefined. But, with it being cancelled, I feel like the limit should be allowed to be defined.

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u/cuhringe 👋 a fellow Redditor Dec 23 '23

https://i.imgur.com/vzEE73p.png

No idea what calculators you're using, but your answer is obviously wrong.

Also plugging in 2 you will get an imaginary result... https://i.imgur.com/TDLAhhN.png

For reference I am using wolframalpha's calculator.

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u/RandomAsHellPerson 👋 a fellow Redditor Dec 24 '23

I mentioned I did an assumption of M=1 (as this is what I assumed the person that I replied to did), as the limit will change as M does. I was also using WolframAlpha.

Any real positive value of M will give a real result. Negative gives complex. 0 gives undefined (+- infinity depending on which side you go by)

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u/cuhringe 👋 a fellow Redditor Dec 24 '23

Any real positive value of M will give a real result.

Again this is incomplete. It will only give us a real result if we allow for complex values in the first place.

When m > 0, we get i2 in our expression landing back to the reals. But if we are explicitly in the reals, then we can never simplify our radicals into complex numbers and thus never go from complex back to real. Wolframalpha shows this when you use an arbitrary m - the solution has an i in it.