Let's Talk About Limits

rubah · 03-05-2008, 07:54 AM

Oh man I hate them.

After playing with my calculator, I have found out that the limit as x->∞ of the arctan(x) is π/2, the arcsec(x) as x->1 = ∞, and little else.

Anything else I should be aware of before trying to do crazy-seeming Improper Integrals problems that look divergent but they actually converge because goshdarn it, wouldn't you just know the arctan(∞) happens to be π/2?

Momiji · 03-05-2008, 09:01 AM

Okay...what the hell is this? I think my brain just short-circuited reading that.

I'm not good at math.

Vivisteiner · 03-05-2008, 09:52 PM

Wiki can help: Trigonometric functions - Wikipedia, the free encyclopedia

Because I cant. What level is this around?

And what the hell is up with all this trigonometry crap? It was so easy when you just had sin, cos and tan. Then they add csc and cot which is just about all right. And now they have arcsin, arctan, arccos, arccsc, arcsec, arccot!

Whats the point?

Is it just for simplification or something?

Flying Mullet · 03-05-2008, 09:57 PM

Originally Posted by Vivisteiner ^

Wiki can help: Trigonometric functions - Wikipedia, the free encyclopedia

Because I cant. What level is this around?

And what the hell is up with all this trigonometry crap? It was so easy when you just had sin, cos and tan. Then they add csc and cot which is just about all right. And now they have arcsin, arctan, arccos, arccsc, arcsec, arccot!

Whats the point?

Is it just for simplification or something?

arcsin is the inverse function of sin; arctan is the inverse function of tan, etc... Once you understand the relationships between them, they're quite simple, actually. And csc = (1/sin), cot = (1/tan) which are pretty straight forward too.

rubah · 03-05-2008, 10:58 PM

oh just wait until you get to the hyperbolic trig functions :sarcasm:

you learn trig stuff in trig, and then you use it in calculus because it makes integrating crazy easier/possible. The problem in question was the integral from 0 to ∞ of one over the sum of two squares, which reeks of the arctangent.

Vivisteiner · 03-05-2008, 11:27 PM

^Integral from 0 to ∞?

Thats gotta be ∞!

Ehhh, I find differentiation and integration so boring. I mean who gives a damn whether you use forward or reverse substitution, or integration by parts or implicit differentiation. Its not hard, just boring.*

Thats just my rant. Stupid C3 Maths module.

*Actually, it is hard when you dont have a clue what your teacher is on about and then you get set some hw that just screams 'waste of my time!'

rubah · 03-05-2008, 11:34 PM

They're not boring because you can do crazy stuff with them xD Also it's π/2 at ∞

it never gets bigger than that.

qwertyxsora · 03-05-2008, 11:40 PM

Don't forget that arcsin and Arcsin are different things. arctan is the whole inverse relationship, while Arcsin is only the part that is a function.

Momiji Site Staff Allegro Cantabile Location: Loli, loli, loli, get your adverbs here~	#2 (permalink) Okay...what the hell is this? I think my brain just short-circuited reading that. I'm not good at math.
03-05-2008, 09:01 AM

rubah Site Staff Cid's Knight I am not a committee! Location: Don't forget you're not alone	#5 (permalink) oh just wait until you get to the hyperbolic trig functions :sarcasm: you learn trig stuff in trig, and then you use it in calculus because it makes integrating crazy easier/possible. The problem in question was the integral from 0 to ∞ of one over the sum of two squares, which reeks of the arctangent.
03-05-2008, 10:58 PM

rubah Site Staff Cid's Knight I am not a committee! Location: Don't forget you're not alone	#7 (permalink) They're not boring because you can do crazy stuff with them xD Also it's π/2 at ∞ it never gets bigger than that.
03-05-2008, 11:34 PM

qwertyxsora Ivysaur! Leech seed! Location: Look in the tall grass	#8 (permalink) Don't forget that arcsin and Arcsin are different things. arctan is the whole inverse relationship, while Arcsin is only the part that is a function.
03-05-2008, 11:40 PM