TrueTears question thread

[Over9000]

No probs, people make mistakes, thats what were here for 

[TrueTears]

Let w = 2z. Describe the locus of w if z describes a circle with centre (1,2) and radius 3.

Basically, I did this question by inspection. w is just z doubled. so the new centre is (2,4) and radius is 6.

But how do you do this problem algebraically?

[kamil9876]

Write out an equation for z. and sub in z=w/2.

|z-1-2i|=3
|w/2 -1-2i|=3
and now multiply everything by 2 to get w by itself.

[TrueTears]

Write out an equation for z. and sub in z=w/2.

|z-1-2i|=3
|w/2 -1-2i|=3
and now multiply everything by 2 to get w by itself.

nice thanks kamil.

[/0]

haha good solution kamil, much better than my solution

[kamil9876]

lol may i see it? curious

[TrueTears]

lol just stomped on this Q over C

Factorise

[Damo17]

lol just stomped on this Q over C

Factorise

http://vcenotes.com/forum/index.php/topic,10575.0.html

[TrueTears]

thanks damo !

[TrueTears]

Just this one question, bit stomped on it.

Thanks guys

[kamil9876]

a good place to start is to start with dilations in x axis. The thing has a domain that is 6 units long. Whereas the original domain is 2pi/3 units long. SO the dilation mustve been 6/(2pi/3) and so the value of b is the reciprocal of that.



Due to the symetricity of the graph, the endpoints of the domain are the same. And they are simply sec(pi/3)=2. You want the endpoints to be at zero so you shift the graph 2 units down. Then you translate 3 units to the right. Then reflect in y axis and you've got the basic shape, all you have to do now is amplify (dilate in y axis to get a maximum of 4.

[TrueTears]

thanks kamil for that

Now a very interesting question:

Implicit differentiate with respect to x



solving for leads to

HOWEVER the original equation can be simplified to

yet the derivative says ?

Thanks guys!

[kamil9876]

in ur implicit differentiation u divided both sides by y-x, which is the same as dividing by 0.

Consider the argument:



divide both sides by y-x:

and hence y does not equal x.

The flaw is in dividing both sides by an unkown quantity without ensuring it was non-zero.

btw, if y=x u get 0/0 which isnt as bad as 1/0. If you ever encounter 0/0 u most likely did that by having a true statement such as ab=c (where a and c are zero) and divided both sides by a to get b by itself. Hence try to trackback to any division.

[TrueTears]

Thanks for that, but how do I implicit differentiate it without dividing by 0?

[kamil9876]

just do a quick test to see if the thing u are dividing is not zero(that is generally true, not just implicit differentiation):

say:


I can divide both sides by e^x because i know it is never 0.

However if we have:

You must take into account the possibility that cos(x)=0 Hence do a seperate solution for the case cos(x)=0 and a seperate solution if it does not equal 0(where division is good).