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Hey

What's your question?

ok I will provide the example :D just give me a sec

\[\int\limits_{1}^{\infty}(x ^{2}-6x+1)/(x ^{2}+4)\]

I seriously dont understand the whole concept :P

No, it doesn't.

can you explain ur reasoning?

= -x^-1

Evaluated at the endpoints gives us?

-1/a +1

Perfect. Now apply the limit. Does it converge, and if so, to what?

it converges it equals 1

right?

Jemurray?

Well = lnIxI

Okay, keep going :)

lnIaI-lnI1I =lnIaI

And if you apply the limit then we see it diverges

Indeed it does. You seem to have it down pretty well. :)

well this is easy but I am getting confused with this one

I also dont know when a function is slowly hitting zero as it approaches infinity

LIke how wld you know if it is approaching slowly or quickly?

N must be greater than 1. But i know that because my book tells me so

what wld happen if n would be equal to 1?

That was the second integral you calculated :)

oh lol I see

oh i see yes thats clear

but lets return to the original problem

How would i know like which part of the function dominates?

What is the limit of the integrand as x approaches infinity?

of which function?

Your original problem.

well there are so many x's in this problem. Some will be negative and others will be positive

Try dividing top and bottom by x^2 and then taking the limit, ignoring terms that go to zero.

sorry what do u mean?

Well now i realized that when x approaches infinity x^2 dominates the numerator

Dividing yields
\[ \frac{1 - 6/x + 1/x^2}{1 + 4/x^2} \]

the others are insignificant in comparison

Yes, that's correct. So what's the limit?

x^2/x^2=1
so it equals =x and so it diverges as x approaches infinty

what i meant to say was that the integral of 1=x

So how wld you solve it?

I wanna learn because i dont feel like i am doing it correctly. I am missing the basics in this area

It's not a question of solving it or not. It doesn't converge, that's the end of the story.

LOL hehe ok got it

so for example \[\int\limits_{50}^{\infty}dx/x ^{3}\]

This we can see automatically converges

since as x becomes larger than 1/x^{3} is getting closer to 0

ohhhhh i seee fine

Thanks for your help

I am just trying to logically see this in my brain

So that I will be able to solve on my own

ok gn. If I have any more questions I will be back :D

I hope u dont mind

ok Great thanks

I finished my hmwrk So i am heading to bed :D

I dont need anymore help :D