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Mathematics: Post your doubts here!

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When the tangent is parallel to the y axis, the dy/dx is infinity. To express infinity= 1/0
So we equate the dy/dx=1/0
y/[x(3y^3-1)] = 1/0
cross multiplying:
x(3y^3-1)=o

3y^3-1=0
y= cube root of (1/3)
y= 0.693

Substitue this value into x(3y^3-1)=o to find the x coordinate.

how did u do i) part? I did but I didn't get the answer
 

Jaf

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When the tangent is parallel to the y axis, the dy/dx is infinity. To express infinity= 1/0
So we equate the dy/dx=1/0
y/[x(3y^3-1)] = 1/0
cross multiplying:
x(3y^3-1)=o

3y^3-1=0
y= cube root of (1/3)
y= 0.693

Substitue this value into x(3y^3-1)=o to find the x coordinate.
The issue I had with the answer to this is that instead of rounding off to 0.693 before substitution into the equation, I continue to use cuberoot of 1/3, and end up getting a different answer for the x coordinate (the difference is quite a bit actually). Confusing. :S
 
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You found your limit in part i, which was 1/4 π. Now as you can see, before the area under the curve was denoted by A. Now they equated the integral to 40A, which means the area under the curve is 40 times bigger. Hence the limits are to be multiplied by 40.
kπ= 1/4π *40
k=10
 

Jaf

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Dude, just multiply your two answers from part i) to get one quadratic factor and find the other one by (Ax^2 + Bx + C) inspection.
That is, the roots you get in i) are 1 - √2 i and 1 + √2 i. So the factors become (x-1+√2 i)(x-1-√2 i). You multiply the brackets and you'll see everything in terms of 'i' gets cancelled to give you a quadratic factor of x^2 - 2x +3.

If you still don't get it, let me know I'll post a screenshot.
 
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Never really understood what they did. I would want some help in this question as well!

November 2012 P3, was the hardest paper which CIE released since 2002 ! :eek:
Lets hope we get one which will be much easier tomorrow so that we all can ace Insha Allah :)
 
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t
November 2012 P3, was the hardest paper which CIE released since 2002 ! :eek:
Lets hope we get one which will be much easier tomorrow so that we all can ace Insha Allah :)
the easier the harder to ace to harder the easier to ace
 

Jaf

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You found your limit in part i, which was 1/4 π. Now as you can see, before the area under the curve was denoted by A. Now they equated the integral to 40A, which means the area under the curve is 40 times bigger. Hence the limits are to be multiplied by 40.
kπ= 1/4π *40
k=10
I see. Thank you so much.
 
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