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Please could you tell me how to integrate tan^3[x] without integration by parts.

i know that tan^2x = sec^2 x - 1

thanks in advance.

thanks. ive worked it out now...

This is probably really easy for all you guys, but I can't see the answer:

Given that log 2 = 0.3, show that log 5 = 0.7

Thanks in advance.

^assuming that is correct^

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And it does have one use: I got an offer from a uni based on an interview where I had to prove that (2^0.5) was irrational' date=' and I used that proof .

 

Ollie[/quote']

 

How exactly did you use this proof because if you use this proof for 2^0.5, then in Fermat's last theorem, n=2, which doesn't contradict Fermat's last theorem.

the thing is, this was set as a sort of 'brainteaser' question, so i was wondering if there was a simple, almost 'sneaky' way of doing it...

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- i think...!

Does anybody have any ideas on how to work out [imath]\sqrt{0.9}[/imath] without a calculator (to approx 10 d.p.)?

I know there are a few methods for working out for working out square roots by hand, but i was wondering if there was a cleverer/easier way of doing it.

why does women = time * money and not women = time + money?

- that's true. I originally saw this proof for 'teletubbies', for which it worked, because they were the PRODUCT of time and money (hence multiplication)...

[math]\pi=\frac{diameter}{circumfrence}[/math]

That is all.

actually' date=' [math']\pi=\frac{circumference}{diameter}[/math]

i was wondering if somebody had any ideas about this:

the gradient of a horizontal line = 0

the gradient of a vertical line = infinity

but the product of the gradients of perpendicular lines is -1

so does that mean that 0 x infinity = -1 ???

... or is there something in the proof for the product of the gradients equalling -1 which excludes it for these values?