HSC 2012 MX1 Marathon #2 (archive) (1 Viewer)

[nightweaver066]

Re: HSC 2012 Marathon

Lol what?

http://community.boredofstudies.org/showthread.php?t=274161

 

[bleakarcher]

Re: HSC 2012 Marathon

Lol what?

http://community.boredofstudies.org/showthread.php?t=274161

bahahaha^, i knew it. nightweaver, just accept it, please.

 

[bleakarcher]

Re: HSC 2012 Marathon

parabola

next question:
simplify :
sin(A+B)sin(A-B)+cos(A+B)cos(A-B)

restating this.

 

[nightweaver066]

Re: HSC 2012 Marathon

parabola

next question:
simplify :
sin(A+B)sin(A-B)+cos(A+B)cos(A-B)

cos(A + B - (A - B))

= cos(A + B - A + B)

= cos2B

@Carrot (your first post), i believe that's what happened to my thread lol.

 

[deswa1]

Re: HSC 2012 Marathon

http://www.wolframalpha.com/input/?i=y%3Dx^3%2Fx

 

[bleakarcher]

Re: HSC 2012 Marathon

http://www.wolframalpha.com/input/?i=y%3Dx^3%2Fx

yeh i typed it up and noticed. But i dont see how that is right.

 

[deswa1]

Re: HSC 2012 Marathon

Consider the straight line y=x. You can multiply the RHS by x/x without changing its value. Thus the straight line becomes y=x^2/x which suddenly can't have a value of 0, even though the line hasn't changed and its still defined at x=0

 

[AAEldar]

Re: HSC 2012 Marathon

Consider the straight line y=x. You can multiply the RHS by x/x without changing its value. Thus the straight line becomes y=x^2/x which suddenly can't have a value of 0, even though the line hasn't changed and its still defined at x=0

No no no. You cannot just divide by x and assume that it takes on all real values. As soon as you divide by x you're assuming that it can't equal zero.

 

[mirakon]

Re: HSC 2012 Marathon

No no no. You cannot just divide by x and assume that it takes on all real values. As soon as you divide by x you're assuming that it can't equal zero.

Yep because x can be any value including zero so multiplying by x/x is erroneous

 

[mirakon]

Re: HSC 2012 Marathon

(i think)

 

[deswa1]

Re: HSC 2012 Marathon

Yep because x can be any value including zero so multiplying by x/x is erroneous

Yep, whoops didn't think of that. Why then does wolfram show the curve continuous at 0?

 

[Carrotsticks]

Re: HSC 2012 Marathon

Yep, whoops didn't think of that. Why then does wolfram show the curve continuous at 0?

Because x=0 is an infinitely small point so barely noticeable.

 

[barbernator]

Re: HSC 2012 Marathon

sorry for turning this thread into a pedantic fest, next question!

solve for x.

e^(2x) - 7e^(x) + 9 > 0 (difficulty: moderately intriguing)

highlight below for the answer:

the answer is in your head

 

[Timske]

Re: HSC 2012 Marathon

sorry for turning this thread into a pedantic fest, next question!

solve for x.

e^(2x) - 7e^(x) + 9 > 0 (difficulty: moderately intriguing)

highlight below for the answer:

the answer is in your head

Is it
x < Ln(3.5 - sqrt(13)/2) and x > Ln(3.5 + sqrt(13)/2)

lol

 

[barbernator]

Re: HSC 2012 Marathon

Is it
x < Ln(3.5 - sqrt(13)/2) and x > Ln(3.5 + sqrt(13)/2)

lol

correct

 

[Timske]

Re: HSC 2012 Marathon

Given f(x) = arccos(1/x)

State it's domain

 

[Carrotsticks]

Re: HSC 2012 Marathon

Given f(x) = arccos(1/x)

State it's domain

What would you say the difficulty is?

 

[barbernator]

Re: HSC 2012 Marathon

Given f(x) = arccos(1/x)

State it's domain

x>1, x<-1 (greater or equal)

 

[Timske]

Re: HSC 2012 Marathon

Medium

 

[Timske]

Re: HSC 2012 Marathon

x>1, x<-1 (greater or equal)

Nice