royalchicken?...

differentiate cos2x from first principles. so then, why does
lim
h->0 ((sin2h)/h)=2 ?...

i was typing it all out then lost it all and couldn't be bothered typing it up again...😛

Er... what's your definition of sin? If it's the power series, then it's because all the terms of sin2h/h tend to zero except 2h/h, which is 2.

I get the feeling I'm missing something here 😕

this isn't so much a *problem* as a well, problem 😛 it came up in maths the other day, and my teacher anounced that e had no idea why this was, and neither did anyone else in the maths department...and i have no idea what you mean about power series and sin 😕

Hey genius. d(sin 2h)/dh = 2cos2h. Since sin2h--->0 as h--->0, and h--->0 as h--->0, just apply l'Hopital's rule and you get:

lim sin2h/h = 2 lim cos2h = 2.

Originally posted by royalchicken
Hey genius. d(sin 2h)/dh = 2cos2h. Since sin2h--->0 as h--->0, and h--->0 as h--->0, just apply l'Hopital's rule and you get:

lim sin2h/h = 2 lim cos2h = 2.

'Tis fairly standard, and it explains this. If the limit would be an indeterminate form of the right type (inf/inf, 0/0, 0*inf), then:

lim f(x)/g(x) = lim f'(x)/g'(x)

with as many repetitions as needed.

Originally posted by Acolyte
Er... what's your definition of sin?

You can also use Taylor.
f(x) = f(0) + x * f'(0) + 1/2 x^2 f''(q) for some q in [0,x]

then sin x = sin 0 + x cos 0 + 1/2 x^2 sin q = x + 1/2 x^2 sin q

then (sin x)/x = 1 + 1/2 x sin q --> 1 if x-->0

sin(2h)/h = (2 sin h cos h)/h = 2 (sin h)/h cos h = 2 * 1 * 1 = 2

Indeed you can. Good show. I think this was mentioned before, and indeed I prefer to think of the circular functions in terms of their Maclaurin series, because for complex arguments the standard definition of say, sin z becomes rather meaningless.

Originally posted by royalchicken
Acolyte, I do believe this belongs in the thread on God😉

Colin, you've used the wrong thread. Take two cards.

~Chairman Chicken 😛

You know guys, sometimes I think you just post bogus stuff to make everyone else that comes in here feel so stupid! 🙄 Hahahaha, all these rules I have never heard of and all these nuts equations! My brain starts wimpering on the spot when I see that stuff! Hahahaha, Just Kidding guys. I'm actually jealous that I can't help out with this stuff! Carry on. 😀