Is this correct?
Thanks in advance!

Is this correct?
Thanks in advance!
It does not equal infinity. But if you meant that it diverges, then yes, it does.
I would think it is undefined? My teacher said it is equal to infinity because 5x approaches to positive infinity faster than x approaches to negative infinity and I did not agree because it comes out to be infinity minus infinity.
If it is not undefined, what is it? If it is undefined, how could I better express to my teacher that they're incorrect?
Integrals can be broken into pieces, so:Originally Posted by m84uily
If then you can reduce that to , which obviously diverges.
(Edit: Sorry, forgot to divide by 2.)
Originally Posted by MagiMaster
Which is undefined? Maybe I'm misunderstanding the word "divergent" I take it to mean that the sums do not approach some limit. If that's right then I understand its being divergent, I just want to know if my teacher's reasoning is incorrect or not.
Your teacher isn't exactly wrong, just not exactly accurate. It'd be more proper to say that:
Infinities generally don't make much sense outside of limits, so without being more precise, it'd be hard to say for sure what's right or wrong.
Okay! Thanks :DOriginally Posted by MagiMaster
I believe all parties here, including your teacher, do not understand the meaning of the phrase
.
What this means is that
as and independently of each other. It is not sufficient to set a = b and take the limit.
In this particular example, the integral is undefined.
salsaonline, unsurprisingly, is correct.Originally Posted by m84uily
So are you.
Are you taking a highschool calculus class ? If so, there is probably little that you can do to convince your teacher. If not, find a better college.
You will see such questions treated properly, and in some depth, in a university class on real analysis. If the integrand is nonnegative, things are fairly simple. If not, the issues can be subtle.
Yeah, I'm in high school, I guess I'll give up on trying to convince my teacher and just do things their way for marks. I'll be looking forward to that class on real analysis :DOriginally Posted by DrRocket
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