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Mathematics Extension 2 - 2016 Post-HSC Exam Thoughts (1 Viewer)

InteGrand

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And 14aii
14 a(ii): cos(x) is odd about x = pi/2, so raising cos(x) to an odd power (or more generally, applying any odd function to it) will maintain this property.

In other words, (cos(x))^(2n-1) is also odd about pi/2 for any positive integer n, so integrates to 0 over 0 to pi (integrating a function over an interval where it's odd about the midpoint is 0, since the area above the x-axis is cancelled out symmetrically by that below).

 
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calamebe

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Answer to q 10? 12 d ii), 13 c ii)?
For 12 d ii), I just subbed in y = c^2/x and rearranged to get a quadratic, then used the product of roots. 13 will take too long to type out, but just set T2 greater than T1 and solve for w.
 

calamebe

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Yeah I just showed that the discriminant was equal to zero, and hence that was a double root of the derivative, and thus as it is also a root of the function, it must be a triple root.
 

Glyde

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i thought it said 'prove it is a double root', so i showed that the derivative could equal zero. will i get some marks?
 

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