I know that, when x approaches 0, sinx=x and tgx=x. But, doing

>how does a periodic function behave as it tends to infinity
:thinkan:

>>8962930
Just expand them yourself, it's just a Taylor series.

>>8962935
Actually, that part was utterly retarded, ignore that. To be fair tho, I wasn't asking only about the periodic functions, but I guess the other ones would be easy to solve.

>>8962936
I honestly have no idea how to do that, and I'm not sure I have time to learn now. I've got a lot of ground to cover until the 15th, and that would take a bunch of time, and in return I could realize that functions listed here are the only ones.

But if I don't find some useful list, yeah, I might have to resort to learning how to do what you just said.

>>8962942
Most of the small angle approximation or small argument approximation come from either the Taylor expansion (usually functions like exp, trig functions, logs), or the generalized binomial expansion (usually expressions of the form (1+x)^r with r any real number). Arguably the large argument approximations come from those too.

I've never in 3 years doing maths/physics at uni have had to use small argument approximations for something other than cos or sin and binomials, and I'm pretty sure such a thing does not exist for fast growing functions like log or exp

>>8962942
So I've found another one:
(1+x)^r=1+rx for x approaching 0.
Are there more?

>>8962948
Oh but there are! For example the one I already mentioned: e^x-1=x for x->0

Also my professor is a sadist, and gives us limits like:
lim(x,y)->(inf,inf) arcsin((x+y)/(x^2+y^2)). Took me half an hour of precious time to find out that he wants me to approximate arcsin(A)=A for A->0.

>>8962942
>I honestly have no idea how to do that
Okay, in that case use wolfram alpha:
http://www.wolframalpha.com/input/?i=expand+(1-x)%5Er++about+x%3D0

>>8962936
I guess I've found it:
http://www.astro.umd.edu/~hamilton/ASTR498/expansions.pdf
These are all it seems.

I'm just wondering one more thing. My friend here (who's notebook I'm using) seems to have marked down some approximation using sqrt(1+x) or maybe even (1+x)^(1/n) where n is not only 2, but neither me or him can make it out what is written. Do you know which one is that?

>>8962954
I guess, but I find the Taylor series in one or two variables is probably a better way of finding these limits, rather than memorizing every single possible trick.

Maybe something to take into account is that inverse functions (like arcsin), are just reflections of their respective function on the y=x line, so if sin is approximately x, then reflection about the line still gives approximately x

>>8962949
just look up the taylor series of functions,
drop all terms past the first non-constant term and that's what it behaves like as it goes to zero

i could do a google image search for taylor series of common functions and post it here, but it just feels too much like spoonfeeding. the information is readily available m8.

>>8962966
>>8962967
Thank you guys that was so helpful! No need to do the search for me, the fact that I need to look at first non-constant term was all I needed. Thanks a lot, again!

>>8962977
yeah, you probably know this but i suppose it's worth mentioning that if your leading term has a negative exponent on the variable then it blows up at 0