Possible proof?

1. Jan 12, 2010

evagelos

possible proof??

Can we prove that the limit of :

$$lim_{n\to 0}\frac{sinx}{x} =1$$

By using the ε-δ definition??

2. Jan 12, 2010

Feldoh

3. Jan 13, 2010

rochfor1

Re: possible proof??

I don't believe the Squeeze Theorem works too well for this one, because $$\lim_{ x \to 0 } \pm \frac{1}{x}$$ does not exist. The standard proof of this fact would cite either a geometric argument, Taylor series, or L'Hopital's theorem.

4. Jan 13, 2010

dacruick

Re: possible proof??

i dunno, take the derivative and set x equal to 0 and you get 1. thats proof enough for a physics forum

5. Jan 13, 2010

breedencm

Re: possible proof??

d/dx sin(x) @ x = 0, is defined as: lim x->0 [sin(x) - sin(0)]/x = lim x->0 sin(x)/x.

Basically, you can't assume that this limit is 1 to prove that this limit is 1, unless ofcourse you can prove that d/dx sin(x) = cos(x) and consider this as a special case (however, you will come to find that hidden in this proof contains the question being asked).