HSC 2016 Maths Marathon (archive) (1 Viewer)

[davidgoes4wce]

Re: HSC 2016 2U Marathon

my bad.

y ' = lim (h → 0) (f(x+h) - f(x)) / h
= lim (h → 0) (1/(x+h) - 1/x) / h
= lim (h → 0) (x/x(x+h) - (x + h)/x(x + h)) / h
= lim (h → 0) (-h / x(x + h)) / h
= lim (h → 0) -1 / x(x + h)
= 1/ x²

You forgot the negative in the last step

My attempt:

 

[Green Yoda]

Re: HSC 2016 2U Marathon

You forgot the negative in the last step

My attempt:

Oh yeah shît, fixed it.

 

[kawaiipotato]

Re: HSC 2016 2U Marathon

Question :

 

[leehuan]

Re: HSC 2016 2U Marathon

Question :

Your question got a bit messed up.



Please fix

 

[kawaiipotato]

Re: HSC 2016 2U Marathon

Your question got a bit messed up.



Please fix

Yep fixed it haha

 

[InteGrand]

Re: HSC 2016 2U Marathon

Question :

Are you sure you meant sum, or did you just mean limit of that expression? Because that sum clearly will not converge, as can be seen by using the integral test ( https://en.wikipedia.org/wiki/Integral_test_for_convergence ).

 

[leehuan]

Re: HSC 2016 2U Marathon

Are you sure you meant sum, or did you just mean limit of that expression? Because that sum clearly will not converge, as can be seen by using the integral test ( https://en.wikipedia.org/wiki/Integral_test_for_convergence ).

I remember the result for the nth partial sum and that definitely doesn't converge. Was wondering same

 

[kawaiipotato]

Re: HSC 2016 2U Marathon

Are you sure you meant sum, or did you just mean limit of that expression? Because that sum clearly will not converge, as can be seen by using the integral test ( https://en.wikipedia.org/wiki/Integral_test_for_convergence ).

Oops, yeah, changed n to 80

 

[davidgoes4wce]

Re: HSC 2016 2U Marathon

Find the volume of solid between the 2 curves rotated about the y-axis.

 

[leehuan]

Re: HSC 2016 2U Marathon

Find the volume of solid between the 2 curves rotated about the y-axis.

Still an unanswered question though.

But nice, cause it's y-axis. To rearrange y=x^2-2x needs some very clever completing the square or the quad formula

 

[sharoooooo]

Re: HSC 2016 2U Marathon

Long time no maths gg
Can't finish it :/

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[InteGrand]

Re: HSC 2016 2U Marathon

Find the volume of solid between the 2 curves rotated about the y-axis.

Is this from a 2U Paper/Textbook? If it's from 4U, you can easily do it using cylindrical shells.

 

[leehuan]

Re: HSC 2016 2U Marathon

 

[RachelGreen]

Re: HSC 2016 2U Marathon

What's the Shells Methods? Can you explain, just wondering

 

[davidgoes4wce]

Re: HSC 2016 2U Marathon

I like cylindrical shells but that was a long time ago in uni.

 

[InteGrand]

Re: HSC 2016 2U Marathon

What's the Shells Methods? Can you explain, just wondering

It's a HSC 4U technique of calculating volumes. It's not required for 2U or 3U.

(You can find out about it here: http://www.stewartcalculus.com/data...texts/upfiles/3c3-Volums-CylinShells_Stu .pdf )

 

[leehuan]

Re: HSC 2016 2U Marathon

What's the Shells Methods? Can you explain, just wondering

We maintain that y = f(x)
i.e. x is not a function of y

Just reiterating first that you'll see this later in 4U. But it's not in 2/3U.

Using the normal method, we rotate about the x-axis. i.e., we rotate perpendicular to y
Using shells, however, we rotate about the y-axis. i.e., we rotate parallel to y.
It's an alternative to rearranging y=f(x) to make x the subject

(Also, in 4U, you find you don't have to rotate about the coordinate axes. You can rotate about, say, the line x=-1/2).

(Sophisticated explanation - see above)

 

[leehuan]

Re: HSC 2016 2U Marathon

I like cylindrical shells but that was a long time ago in uni.

If you go on to teaching 4u eventually, you will have to experience it again.

 

[davidgoes4wce]

Re: HSC 2016 2U Marathon

If you go on to teaching 4u eventually, you will have to experience it again.

Sssshhhhh, don't tell everyone I want to be a teacher. I'm not that good yet

 

[Glyde]

HSC 2016 2U Marathon

Calculate the area between the curve (4-x^2)^(1/2) and the x-axis for the 1st quadrant only.


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