Quake3World

How can lim[(sin x) / x], when x approaches 0, be 1?

sin 0 would be 0, 0/0 is imaginary. Yet it clearly states in my book that the answer is 1. How?

0/0 is either infinite or undefined, not imaginary
Just plugin a couple numbers to see the progression towards 1.
sin(0.5)/0.5 = 0.95885107720840600054657587043114
sin(0.4)/0.4 = 0.97354585577162622916577939198926
sin(0.3)/0.3 = 0.98506735553779858368440248561676
sin(0.2)/0.2 = 0.99334665397530607729706313559195
sin(0.1)/0.1 = 0.99833416646828152306814198410622
sin(0.01)/0.01 = 0.99998333341666646825424382690997
sin(0.001)/0.001 = 0.99999983333334166666646825397101

nice forums moron...nice traffic...get a life...

1. f(0)=sin(0)/0 is not defined - this is why you do the limes

2. proof: http://www.mathematik.net/0-calc_site_d ... mSinX.html

math is gay...completely useless...any questions?

At the same time I understand these when I'm at school, it looks totally fucked up when I'm home.

Deji wrote:How can lim[(sin x) / x], when x approaches 0, be 1?

sin 0 would be 0, 0/0 is imaginary. Yet it clearly states in my book that the answer is 1. How?

Have you done much work with limits? Approach it from a graphical point of view, and you'll see that approaching zero from the left or right, the value of sin(x)/x tends to 1. That function is called a sinc function, and here's what it looks like:



Understand that in taking a limit of a function, you're not actually plugging in zero. Rather, you're looking at what happens to the function as the argument approaches zero.

http://mathworld.wolfram.com/SincFunction.html

A little more info on the sinc function.

Thanks, just started learning limits btw.

Calc I or II?

Err, we don't classify the topics under names like that, but it should be calc I from what I've understood of the program in the US.

Interesting, what do you call your math classes and where do you live?

I live in Estonia. We don't actually call our math classes anything, we just have 'maths' and simply talk about different topics. Everything is just one topic: algebra or trigonometry, etc., we don't differentiate between subcategories like precalculus algebra and stuff like that. Maybe they do in university, but not in high school.

um my college didnt have names like that for Calc, only one 3 part single variable series and then a branching procession of other math classes you could take in many different orders and what not

btw sinx/x is a 0/0 limit which alows you to use L'Hospital rule:
take the derivative of top and bottom and evaulate the limit again:
df/dx = cosx..... lim [x->0] cosx = 1

you can also use L'Hos when the limits are infinity/infinity and can repeat L'Hos over the same funcation as many times needed to see if you can get a limit out of it

Damn, good point. I forgot all about L'Hopital's Rule.

any links to a proof for the l'hospital rule?

lol proof? i was just like 3 classes away from getting a math major with my CS and i just about always ignored proofs and did quite well

i remember this moronic professor who would spend half a lecture over a single stupid proof that didnt even clear it up bit

stocktroll wrote: you can also use L'Hos when the limits are infinity/infinity and can repeat L'Hos over the same funcation as many times needed to see if you can get a limit out of it

Does it matter whether the infinity is negative or positive? Plus with fractions, can the upper(don't know the term in English) infinity be positive and the lower negative and vice versa?

um, lol i dont remember that much detail. Im going to assume yes for a negetive infinity/positive infinity and vice versa but i cant be bothered to wake up my brain after years of slumber
and im sure a double negative infinity will work for the rule
just google it and im certain there will be some useful info

stocktroll wrote:
i remember this moronic professor who would spend half a lecture over a single stupid proof that didnt even clear it up bit

Oh that guy, that's Professor Justabouteverymathteacherontheplanet.