• We have a few events lined up for the October school holidays!
    Watch this space...

MATH2701 Abstract Algebra/Fundamental Analysis (1 Viewer)

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,805
Gender
Male
HSC
2015
Don't need to show me how to do the entire question if it's way too long. Suggestions are plenty :)





My starting point was just saying f(x) < integrand being 1/t instead of sint/t, but working backwards it just gave me
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,091
Gender
Male
HSC
N/A
Don't need to show me how to do the entire question if it's way too long. Suggestions are plenty :)





My starting point was just saying f(x) < integrand being 1/t instead of sint/t, but working backwards it just gave me
You can try using integration by parts.
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,454
Location
Outside reality
Gender
Male
HSC
2016
Don't need to show me how to do the entire question if it's way too long. Suggestions are plenty :)





My starting point was just saying f(x) < integrand being 1/t instead of sint/t, but working backwards it just gave me
I'm getting O(x⁻¹)

Differentiating under the integral sign yields:



Ignore sin x and integrate both sides to obtain an asymptotic...
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,671
Gender
Male
HSC
2007
I'm getting O(x⁻¹)

Differentiating under the integral sign yields:



Ignore sin x and integrate both sides to obtain an asymptotic...
They are both true, your statement is just weaker. IBP usually gains you stuff when you are analysing oscillatory expressions...if you just look at the size of things via absolute values, you ignore a lot of the "cancellation" that comes from the oscillation. IBP picks this up.

Edit: Note that you can recover this improvement from your final expression by integrating the leading order term and NOT ignoring the sin. (The remaining terms have size small enough to not matter.) To deal with this leading oscillatory term you still need to use IBP or something similar, and the differentiation under the integral sign has not saved any time.
 
Last edited:

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,805
Gender
Male
HSC
2015
This was in the final exam and I never figured it out.





with the hint x + y + z = (x+y)/2 + (x+z)/2 + (y+z)/2
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top