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November 11, 2024, 06:42:15 am
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Author Topic: Spesh Qs  (Read 9967 times)  Share 

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/0

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Spesh Qs
« on: July 21, 2009, 10:37:54 pm »
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Let , and let be a zero of .

Show that
Show that is also a zero of .
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kamil9876

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Re: Spesh Qs
« Reply #1 on: July 21, 2009, 10:41:33 pm »
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(1)

multiply both sides by a^2:

(2)

(2) - (1):


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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

TrueTears

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Re: Spesh Qs
« Reply #2 on: July 21, 2009, 10:43:00 pm »
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lol this was itute exam Q
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kamil9876

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Re: Spesh Qs
« Reply #3 on: July 21, 2009, 10:54:30 pm »
0












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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

kamil9876

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Re: Spesh Qs
« Reply #4 on: July 21, 2009, 10:56:34 pm »
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Quote from: TrueTears on July 21, 2009, 10:43:00 pm
lol this was itute exam Q

Orly? meh I was feeling creative today so it worked out, but under exam pressure I don't know if I would have come up with this.
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

/0

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Re: Spesh Qs
« Reply #5 on: July 21, 2009, 10:59:47 pm »
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Quote from: TrueTears on July 21, 2009, 10:43:00 pm
lol this was itute exam Q

Really? I got it from HSC 2008

Thanks kamil :)
« Last Edit: July 21, 2009, 11:15:28 pm by /0 »
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kamil9876

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Re: Spesh Qs
« Reply #6 on: July 22, 2009, 12:39:50 am »
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I just realised I multipled everything by a^2 unnecesarily, look:




Oh and the schoolkid way of doing first part would probably involve the geometric sequence, but what I did is essentially derive the formula for it in disguise. 
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

dcc

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Re: Spesh Qs
« Reply #7 on: July 22, 2009, 05:13:59 pm »
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A 'lazy' way of doing this (i.e. no inspiration whatsoever) is:

.

Notice that . Therefore (You should be able to see that without any evaluation at all, but sometimes it helps just to write everything down).

.
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/0

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Re: Spesh Qs
« Reply #8 on: July 22, 2009, 05:48:18 pm »
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Thanks, it's great to see different approaches, no matter how inspired they are ;p
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Re: Spesh Qs
« Reply #9 on: July 22, 2009, 11:34:03 pm »
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1. Use the method of cylindrical shells to find the volume of the solid formed when the shaded region bounded by

, , and is rotated about the y-axis.

It is given that



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Re: Spesh Qs
« Reply #10 on: July 27, 2009, 09:50:59 pm »
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Describe the key features of

I said "Circle center (0,1), radius 5 in the complex plane"

The answers said "Circle center 0+i, radius 5"

Would my answer be incorrect?
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TrueTears

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Re: Spesh Qs
« Reply #11 on: July 27, 2009, 09:56:51 pm »
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Remember I asked this in class once? Back in good old term 2, and Mr B said we could use Cartesian notation in the Argand diagram.
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Re: Spesh Qs
« Reply #12 on: July 27, 2009, 10:00:15 pm »
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Quote from: TrueTears on July 27, 2009, 09:56:51 pm
Remember I asked this in class once? Back in good old term 2, and Mr B said we could use Cartesian notation in the Argand diagram.

Oh yeah true!
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Re: Spesh Qs
« Reply #13 on: July 27, 2009, 10:49:17 pm »
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Quote from: TrueTears on July 27, 2009, 09:56:51 pm
Remember I asked this in class once? Back in good old term 2, and Mr B said we could use Cartesian notation in the Argand diagram.

It is preferable that you don't, since the axis's of the Argand diagram are defined as Re(z) and Im(z). :)
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Re: Spesh Qs
« Reply #14 on: July 28, 2009, 06:42:52 pm »
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ah i see...


Also: Find for

If I do implicit diff straight away I end up with

If I rearrange so that x is not in the denominator, then implicit diff, I get

Can someone please check this?
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