Question

Prove that the limit of sinx/x as x approaches 0 equals 1

Answer 1

i can do the proof but.......

Answer 2

look in any calc book and you will see it. annoying complicated for such a simple problem. uses "squeeze lemma" lol

Answer 3

I guess L'Hopital rule would work

Answer 4

0/0

so

L'H

Cos(x)/1

Cos(0)=1

Answer 5

Or use L'Hospital's rule:
\[lim_{x\rightarrow 0}\frac{sin(x)}{x} = lim_{x\rightarrow 0}\frac{\frac{d(sin(x))}{dx}}{\frac{d(x)}{dx}} \]
\[= lim_{x\rightarrow 0}\frac{cos(x)}{1} = \frac{1}{1} = 1\]