Dr Finlay

I like the explanation of a limit. One of those golden examples i won't forget, which is useful.

As far as i understand a limit, for example [math]\lim_{x \rightarrow 2}f(x) = 5[/math] means that if you take sufficiently large values close to 2, f(x) approaches 5. This could be thought of graphically. Imagine a straight line through the origin in the positive direction, as you increase the value of x closer to 2, the value on the y axis becomes closer to 5. There are many websites and tutorials which explain limits which i'm sure would be unearthed by a quick google search.

The road to reality by Roger Penrose is stuffed full of equations. There may or may not be something about superstring theory in there. It's probably worth a read though anyway.

Hmm, i think i may have worked it out. I drew a Venn diagram and got

[math]P(A \cap B) = P(B) - P(A \cap B)[/math]

so it follows

[math]P(A \cap B') = P(A) - P(A \cap B)[/math]

i then get the book's answers.

I think i just needed to spend the time to work it out, cheers anyway.

Just done another question, i get a different answer from the book though.

If A and B are two events and P(A) = 0.6 and P(B) = 0.3 and P(AuB) = 0.8 find:-

a) P(AnB)

b)P(A'nB)

c)P(AnB')

For part a) i got 0.1 using the addition rule, which the book says is correct. But for part b) i did

P(A'nB) = (1 - P(A))xP(B)

= 0.4 x 0.3

= 0.12

the book however says the answer is 0.2.

For part c) i did:

P(AnB') = P(A) x (1 - P(B))

= 0.6 x 0.7

= 0.42

the book gives the answer 0.5

Can anyone see what I'm doing wrong?

Thanks alot,

Rob

I got 5*, no age though. 5 stars sounds good though;)

I managed to get that far, but here's an example of a question.

If S and T are two events and P(T) = 0.4 and P(SnT) = 0.15 and P(S' n T') = 0.5, find:

a) P(S n T')

b) P(S)

c) P(S u T)

d) P(S' n T)

e) P(S' u T')

All these questions should be able to be solved using the addition rule. But I can't figure out how to get probabilities of events not occurring from events that do occur, such as a), d) and e).

I'm Rob, from Yorkshire, UK. I'm studying A-levels having just started year 12 doing Physics, Maths, Further maths and History, currently trying to teach myself calculus from Stewart's book. As for interesting facts, i very nearly once met the Queen, and i have a fiver in my right pocket, which also oddly enough, sports an image of the Queen:eek:

You could try and prove riemann and scoop the big prize.

I decided to go over the probability section in my S1 statistics book. However, it seems i've stumbled at the first hurdle. The first exercise is about the addition rule P(AUB) = P(A) + P(B) - P(AnB). There is a question where it asks about the probabilities events not happening, P(A'), P(A'UB), P(A'nB') etc. I know that P(A') = 1 - P(A), but i'm completely stuck on how to get such probabilities of P(A'nB).

Can anyone help unclog my mental block?

Thanks once again,

Rob

Thanks i'll have a look. I understand any number can be made into any other arbitrary number. I was just wondering if there was a way to derive pi from phi or phi from pi. I just thought there must be a way since these 2 numbers have unusual properties. All in all it was just a conversation at school so i wasnt expecting anything. Anyway it's filled in my "learn something new everyday" quota for the week.

Cheers everyone;)

Ah right.

Cheers mate.

As i said, i didnt think there was anything special about the way my equation approximates pi, there are probably an infinite number of ways. I was just wondering if there was an elegant way to connect phi and pi. Maybe i should have just said that at the start:embarass:

Could you rearrange

[math]

\phi^{(\displaystyle\frac{\pi + \phi}{2})}= \pi

[/math]

for [math]\phi[/math]?

Are there any other ways which relate phi and pi, my method is rather poor, and only approximates pi to a few decimal places.

hmm, i dont get [math]x = 2.000811416[/math] when i do pi/phi

I didnt think there was anything special about the equation. Just if there was anything special about the arbitrary number, so that the expression could be completely written in terms of phi and pi, rather than arbitrary numbers.

Me and a few friends at school the other day were wondering if pi and phi were somehow connected, After a while i managed to throw out

[math]\phi^{(\displaystyle\frac{\pi + \phi}{2})}= \pi[/math]

which manages to roughly approximate [math]\pi[/math]. I then found if you did

[math]\phi^{(\displaystyle\frac{\pi + \phi}{x})}= \pi[/math] with [math]x = 2.000811416[/math],

the equation exactly reached [math]\pi[/math]. But [math]x = 2.000811416[/math] seems too random to me, is there any connection between [math]\pi and \phi[/math] that would produce [math]x = 2.000811416[/math]?

On the slight chance you understood what i said, do you know where [math]x = 2.000811416[/math] can be derived from?

Cheers,

Rob

Cheers mate

Would the inverse function of

[math] \displaystyle\frac{1 + e^x}{1 - e^x}[/math]

be

[math]\displaystyle\frac{e^x - 1}{e^x + 1}[/math]

?

Just been working through Stewarts calculus, the book only gives answers to the odd numbered questions. Most of the concepts in the book are pretty new to me, having only just started my Alevels, so i thought it would be best to get as much practice at it as i could.

Cheers,

Rob

Thanks

Aye i see that now. I usually kick myself after failing to spot such things.

Ah brilliant thanks!

Only just started A-level maths so not too familiar with log.

I have come across this question while doing my maths homework:-

Given that 3^x = 9^(y-1), show that x = 2y - 2

Could anyone give me a hint on how to start.

Thank you in advance.

Cheers guys, see where i went wrong now. Having just had a rather long break from maths over the summer months my brain is half asleep most of the time.

y - 2/3 = -2/5 x 5/3

-5y + 2/3 = -5/3 - 2x

-15y + 2 = -5 -6x

6x -15y + 7 = 0