This one is a bit tedious.
http://imgur.com/a/X7CkW
EDIT: Yeah I have no idea how to make the LaTeX valid here imgur will have to do haha. Also I'm still learning so if I can improve anywhere just tell me what to do.
Last edited by calamebe; 23 Jan 2017 at 9:09 PM.
HSC 2017
Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
HSC 2017
Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
By considering
evaluate:
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Using the reflection across the real line with u+x=0, and Glasser's Master Theorem (ceebs showing the intended way but KingOfActing can do that), the integral simplifies completely into:
This can easily be evaluated in the general form using Differentiation Under The Integral Sign.
Last edited by Paradoxica; 15 Feb 2017 at 10:29 PM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Last edited by BenHowe; 22 Feb 2017 at 1:11 PM.
2nd Year Applied Finance/Actuarial Studies @ MQ
GPA 6.77 WAM 87%
Part 1's:CT1,CT2,1/2 CT3,CT7
Last edited by Drongoski; 22 Feb 2017 at 2:15 PM.
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Can't you do two by inspection?
Reckon q2 is 2u?
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There are IB Maths Tutors and there are IB Maths Tutors.
1-on-1 Maths Tutoring(IB & HSC): Epping, Beecroft, Eastwood, Carlingford & Beyond
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There are IB Maths Tutors and there are IB Maths Tutors.
http://m.imgur.com/j3kDVl4
Q1 answer, it's messy so if you can't understand it or read it then tell me. I don't know if there's a faster method but if there is please tell me.
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2nd Year Applied Finance/Actuarial Studies @ MQ
GPA 6.77 WAM 87%
Part 1's:CT1,CT2,1/2 CT3,CT7
Are you sure Q3 has closed form solution?
I don't know what closed form is but you just need to be creative
2nd Year Applied Finance/Actuarial Studies @ MQ
GPA 6.77 WAM 87%
Part 1's:CT1,CT2,1/2 CT3,CT7
For Q4, if you stare at it long enough, you should be able to use reverse quotient rule.
Let y=1+ln x, then y'=1/x
The integrand can be written as
(y-1)/y^2
=(x'y-xy')/y^2.
Now, the answer should be obvious.
Last edited by BenHowe; 24 Feb 2017 at 11:16 AM.
2nd Year Applied Finance/Actuarial Studies @ MQ
GPA 6.77 WAM 87%
Part 1's:CT1,CT2,1/2 CT3,CT7
Last edited by jathu123; 24 Feb 2017 at 11:16 AM.
2017
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