VCE Stuff > VCE Specialist Mathematics
pi's Specialist Maths Questions
ariawuu:
--- Quote from: luken93 on May 16, 2011, 09:29:48 pm ---
--- Quote from: ariawuu on May 16, 2011, 09:17:33 pm ---
--- Quote from: Rohitpi on May 16, 2011, 08:20:22 pm ---
--- Quote from: luken93 on May 15, 2011, 08:58:34 pm ---
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...
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you mean how to work out what tan-1 (3/4) is? use the triangle.. not sure if it answers the question
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Which triangle?
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nvm i was thinking of something else..
pi:
--- Quote from: GuessWho on May 16, 2011, 08:57:14 pm ---Oh god that double derivative question... Spent a few minutes doing that by hand
I saw that in the Math Quest specialist book. I don't really think there is an easy way to do it since most of the time the book would give you the simplest possible answer.
--- End quote ---
I sped things up a little in the end.
1. Quotient rule
2. Rearrange to put denominator on other side
3. Implicit diff and then rearrange for d^2y/dx^2
Still tedious though :(
pi:
A few questions and course queries (not many are on the course, but you never know :P ):
Q1
How would I do this:
Tried integration by parts, couldn't manage to get rid of the trig in the integral >:(
Q2
Is there a general way to solve this (differential equations):
I know its not on the course, but I'm just interested :)
Q3
Is trigonometric substitution on the course? Or is it a purely CAS thing?
Q4
Any way to approach integrating trig powers when the power is a fraction? eg. ?
Another 'just interested' question :)
Q5
This is n00b and trivial, but when sketching , should we sketch the part that is negative on the x-axis too? My CAS doesn't :(
THANKS!
sajib_mostofa:
--- Quote from: Rohitpi on June 20, 2011, 09:30:18 pm ---A few questions and course queries (probably none are on the course, but you never know :P ):
Q1
How would I do this:
Tried integration by parts, couldn't manage to get rid of the trig in the integral >:(
Q2
Is there a general way to solve this (differential equations):
I know its not on the course, but I'm just interested :)
Q3
Is trigonometric substitution on the course? Or is it a purely CAS thing?
THANKS!
--- End quote ---
haha you're an eager one.
1) If you can't get rid of the integral, it might mean that you may have to swap what expressions you assigned to u and dvdx initially i.e trial and error. Or if that doesn't work either, you may need to repeat by parts integration for the second time. *N.B this isnt on the course.
2) I think differential equations might actually be on the course if I remember correctly i.e Newton's rate of cooling . Sometimes, you might have to flip your expression to be able to integrate. i.e say you have dvdt = v^2, you may have to flip and integrate dt/dv = 1/v^2
3) I'm pretty sure trigonometric substitution is on the course. You may be required to do it by hand if its in the first exam.
* Edit: Sorry for the general answers but you latex doesn't seem to appear to me.
pi:
#1 My problem with q1, is that when I integrate it by parts (I tried the swapping v and u too), I get a trig (either sin or cos) in the integral again, and this keeps repeating. I'll research some methods :)
#2 DE's are on the course, but the one mentioned isn't in Mathsquest and Essentials :( I think the tip you gave (a good one!) was for first degree ones. I can't think of a way for 2nd degree as they don't obey fraction laws apparently (could be wrong?)
#3 Thanks! :)
Posed two more qs :)
--- Quote from: Rohitpi on June 20, 2011, 09:30:18 pm ---A few questions and course queries (not many are on the course, but you never know :P ):
Q1
How would I do this:
Tried integration by parts, couldn't manage to get rid of the trig in the integral >:(
Q2
Is there a general way to solve this (differential equations):
I know its not on the course, but I'm just interested :)
Q3
Is trigonometric substitution on the course? Or is it a purely CAS thing?
Q4
Any way to approach integrating trig powers when the power is a fraction? eg. ?
Another 'just interested' question :)
Q5
This is n00b and trivial, but when sketching , should we sketch the part that is negative on the x-axis too? My CAS doesn't :(
THANKS!
--- End quote ---
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