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# S2 June 2013 q9

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1. I don't understand why obtaining the value 8.4126 and 8.8440 by subsitituting in 8.5 and 8.6 shows that the solution is between 8.5 and 8.6, also how do I choose which lambda to sub in?(the one in the equation or the one equal to the equation?)

Unrelated but also in this paper, how do you show variance in graphs of continuous random variable?
2. (Original post by Christina Tiana)
I don't understand why obtaining the value 8.4126 and 8.8440 by subsitituting in 8.5 and 8.6 shows that the solution is between 8.5 and 8.6, also how do I choose which lambda to sub in?(the one in the equation or the one equal to the equation?)

Unrelated but also in this paper, how do you show variance in graphs of continuous random variable?
In part 9iii) You had to show that

If you use

and rearrange to find put it in the form
Spoiler:
Show
then substitute and

when you substitute

So there exists a value of between 8.5 and 8.6 such that
3. (Original post by Christina Tiana)
I don't understand why obtaining the value 8.4126 and 8.8440 by subsitituting in 8.5 and 8.6 shows that the solution is between 8.5 and 8.6, also how do I choose which lambda to sub in?(the one in the equation or the one equal to the equation?)

Unrelated but also in this paper, how do you show variance in graphs of continuous random variable?
Do you remember your C3 stuff? Finding the roots of equations by numerical methods? One of them was showing that and then there must exist a root between a and b? This is the same thing.
4. (Original post by Zacken)
Do you remember your C3 stuff? Finding the roots of equations by numerical methods? One of them was showing that and then there must exist a root between a and b? This is the same thing.
Yes I thought it was a numerical method but I didnt get a sign change, and I actually am quite confused on the topic anyway so I didn't get it, thank you!

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