## Search found 3 matches

- Fri Jul 24, 2015 7:43 pm UTC
- Forum: Mathematics
- Topic: Wanted: Elegant proof of sin(x)/x limit
- Replies:
**49** - Views:
**9158**

### Re: Wanted: Elegant proof of sin(x)/x limit

Youare right - i really messed that one up. Reproof: We have cosx tendingto 1 as x tends to 0, from our above sin(x) <x, and sinx >=0 for x>=0 giving sinx tends to zero. Thus cos^2x tends to 1, and so does cos x(as it is certainly positive). Now take e>0 and x such that cosx>1-e. We want to show (1-...

- Tue Jul 21, 2015 1:29 am UTC
- Forum: Mathematics
- Topic: Prove that 25+8*(n!)) is not square
- Replies:
**10** - Views:
**3437**

### Re: Prove that 25+8*(n!)) is not square

Not got anything proved, but think I have a form that may be easier to deal with. We want to have a^2 =25 +8 n!. Then (a-5)(a+5) =8n!. Now make the transform to b=a-5. Now b(b+10)=8n!. This implies 2|b or b+10, and so 2|b. Now set k=b/2. Then k(k+5)=2n!. In particular, we now know we must group all ...

- Tue Jul 21, 2015 1:09 am UTC
- Forum: Mathematics
- Topic: Wanted: Elegant proof of sin(x)/x limit
- Replies:
**49** - Views:
**9158**

### Re: Wanted: Elegant proof of sin(x)/x limit

From the definition as the side of a right triangle of unit hypotenuse: Lemma 1: sin t<t, t>0 Proof: consider the line y=tx. Then at x=1, we get y=t. But then x^2+y^2=1+t^2>1, and this point is outside the unit circle. But we started inside the circle, and as we have a continuous path, we must cross...