thats just provinf there mutually inverse
e.g.
f(x)=x^3 , therefore f^-1(x)=(3root)x
f^-1[f(x)]=f^-1(x^3)
=(3root)(x^3)
=x
f[f^-1(x)]=f((3root)x)
=((3root)x^3
=x
hope that helps
i think this is it:
let u=sinx , therefore du=cosx.dx
(int) u/(2-u^2)^-0.5
= (int) u(2-u^2)^-1.5
= 2u(2-u^2)^-0.5 + C
=2u/(2-u^2)^0.5 + C
= 2sinx/(2-sin(^2)x)^0.5 + C
it wouldn't hurt.
sometimes you can make some silly errors in tree diagrams and you can use the more complex formulas to back up your answers....thats what i do :)
actually i've seen this come up a bit in past papers (particiularly from private schools)
Given v = dx/dt
d^2x/dt^2 = d/dt(dx/dt)
= dv/dt
= dv/dx.dx/dt
= dv/dx.v
= dv/dx.d/dv(1/2v^2)
= d/dx(1/2v^2)
1.
1 - (12/15 x 11/14 x 10/13)
= 47/91
2.
a) 13/52 x 12/51 = 1/17
b) 13/52 x 13/51 = 13/204
c) 13/52 x 39/51 = 13/68
im pretty sure that they are all right although someone can correct me if im wrong :)
what i've been told, is that it doesn't really matter what idea of your story is, it's the way you describe all the features in the story (if you know what i mean).
and yes, you do have to write a short story in both the trials and the HSC.
i have pretty much finished all my essays for trials.
the only problem i have, is that im not sure if i should memoreise them or just know the main points? And also, should you memorise your thesis or make up a thesis in the exam room that suits the question?
opinions please?
my stress levels are like MORE than "OMFG!!! Totally stressing out... >_<" :spzz:
nah im actually taking it easy atm but ill have to up the ante the next couple of days coz of trials and assessments