Question

Evaluate the following limit or show it does not exist, Show work.

Answer 1

\[\lim_{x \rightarrow 0} \frac{ 1-cosx }{ x }\]

Answer 2

@Chlorophyll @ChmE anyone?

Answer 3

Apply L'hopital rule !

Answer 4

Ill have to look that one up, hah, ill update if I figure it out

Answer 5

I am sorry. I dont know!

Answer 6

Ok I understand that the answer is 0, but why?

Answer 7

lemme play with this...
\[\lim_{x \rightarrow 0} \frac{ 1-cosx }{ x }\]
\[\lim_{x \rightarrow 0} \frac{ 1-cosx}{ x }(\frac{ 1+cosx }{1+cosx })\]
\[\lim_{x \rightarrow 0}\frac{ 1-\cos^2x }{ x(1+cosx) }\]
\[\lim_{x \rightarrow 0} \frac{ sin^2x }{ x(1+\cos x) }\]
\[\lim_{x \rightarrow 0} \frac{ \sin x }{ x } (\frac{ sinx }{ 1+cosx })\]
\[\lim_{x \rightarrow 0} [1* \frac{ sinx }{ 1+cosx }]\]
plug in 0 for x.
\[\lim_{x \rightarrow 0} \frac{ 1-cosx }{ x } = 0\]

Answer 8

Thats exactly where I am, and its freaking me out, lol, thank you