HSC 2013-14 MX1 Marathon (archive) (3 Viewers)

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AnimeX

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Re: HSC 2013 3U Marathon Thread

Question:

[/QUOTE]

Negative as the "area" (not sure how else to put it, but the region there..) between 0.5 and 1 would be negative.

Therefore less than zero.

NEw Question:

Show that the equation lnx + x = 0 has a root between x=0.5 and x=1.
 
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HeroicPandas

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Re: HSC 2013 3U Marathon Thread

Question:

Negative as the "area" (not sure how else to put it, but the region there..) between 0.5 and 1 would be negative.

Therefore less than zero.

Question:

Show that the equation lnx + x = 0 has a root between x=0.5 and x=1.[/QUOTE]

Let f(x) = lnx + x

f(0.5) x f(1) <0

Therefore curve is continous and root lies between



Question:



This is a 3u question
 

AnimeX

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Re: HSC 2013 3U Marathon Thread

@heroicpandas,

was my answer correct for your question?
 

AnimeX

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Re: HSC 2013 3U Marathon Thread

Show that the equation lnx + x = 0 has a root between x=0.5 and x=1.
Let f(x) = lnx + x

f(0.5) x f(1) <0

Therefore curve is continous and root lies between
yup this is correct, but I think it would be better if you subbed in f(0.5) and f(1)

LOL sorry, idk why this quoting stuff isn't working...

Edit: works now..
 

Sy123

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Re: HSC 2013 3U Marathon Thread

@heroicpandas,

was my answer correct for your question?
I think it would be more correct to say that the region bounded by the ln(x) curve from x=1 to x=0.5 lies below the x-axis since,



Therefore the region lies below x-axis, and hence the integral must be negative.

=====



 

HeroicPandas

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Re: HSC 2013 3U Marathon Thread

I think it would be more correct to say that the region bounded by the ln(x) curve from x=1 to x=0.5 lies below the x-axis since,



Therefore the region lies below x-axis, and hence the integral must be negative.

=====



 

AnimeX

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Re: HSC 2013 3U Marathon Thread

I think it would be more correct to say that the region bounded by the ln(x) curve from x=1 to x=0.5 lies below the x-axis since,



Therefore the region lies below x-axis, and hence the integral must be negative.

=====



Oh yep, I agree, "area" wasn't the correct word.

Now your question:



how do you make a new line in Latex?
 

HeroicPandas

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Re: HSC 2013 3U Marathon Thread

Oh yep, I agree, "area" wasn't the correct word.

Now your question:



how do you make a new line in Latex?
U are too pro...



^Sy's great idea!
 
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HeroicPandas

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Re: HSC 2013 3U Marathon Thread

Nice work.

You can make a new lines by typing \\

i.e. [tex ]$Line 1$ \\ $Line 2$ [/ tex]

======



Add both sides with arcsin(x) and i'll let someone else do this
 

Makematics

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Re: HSC 2013 3U Marathon Thread

true! which method were you thinking of when you posted it?
 

Makematics

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Re: HSC 2013 3U Marathon Thread

that's the beauty of integration :) so many methods, and they all work!
 
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