You can make a list of mistakes in another thread then.
Part a)You can make a list of mistakes in another thread then.
This is the marathon. It never was a textbook correction site...
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NEXT QUESTION (since nobody wants to be a dear):
HINT for b) (highlight): Firstly, if you picked a graphical approach to b), well done you took the easy path. Here is the alternate solution:
If you did part a) right, you would know that it is a local minimum. But the minimum turning point is at (0,1), so e^x-x≥1! The trick to notice then is that e^x-x>0 because 1>0, so e^x>x, and thus without a graph you can tell straight away that e^x>x anyway and thus must be the upper curve for the integral.
Be careful, this is a volume between two curves question. NOT AREA!
Yes, this is a circle geometry theorem from HSC 3U ("tangents from a common external point are equal").Am I right in saying the coordinate (4,6) , distance from the tangent to the circle, are the same where it is touching the circle (2 instances)?
If you use a 3u method in 2u, it's still full marks right assuming the working out and answer are right
I know. But if it's at a 2U difficulty then there must be a 2U level solution.
http://m.imgur.com/XXmp2gZ I think I did it rightGreat
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NEXT QUESTION:
(May not have turned out as I planned it to be. Advise if there's a problem)
 A point $P(x,y)$ moves on the number plane such that it's distance from a fixed point $S(7,0)$ is always $4/5$ it's distance from the line $x=37/4$. Find a general equation to the locus of P. \\ b) The locus traced out is actually that of an ellipse, which can always be written in the form $\frac { { \left( x-h \right) }^{ 2 } }{ { a }^{ 2 } } +\frac { { \left( y-k \right) }^{ 2 } }{ { b }^{ 2 } } =1$ where $(h,k)$ is the centre of the ellipse. Find the centre of this ellipse. )
Pretty sad how this hasn't been answered yet but it could just be cause of the lateness this topic is typically taught so just this time I'm gonna steal a 16er question.
The second integral can be re-interpreted as the integral of the sideways parabola from x=5 to it's vertex.
 By evaluating the integrals, show that $\\ \int _{ -2 }^{ 2 }{ \left( 4-{ x }^{ 2 } \right) \, dx } =2\int _{ 5 }^{ 9 }{ \sqrt { 9-x }\, dx } \\ $b) Explain this result geometrically.$)
