Question

Finding Limits: find limit as x approaches 0 of (cos 2x - 1)/(3x)

Answer 1

is that:\[cos(2x)-1\]???

Answer 2

If so, you can work a Laplace, 1 iteration should get that denom to 3

Answer 3

-2sin(0)/3 = 0

Answer 4

Yes, sorry, that is cos (2x) - 1/3x....and I'm sorry I don't know what you mean by 1 iteration or Laplace?

Answer 5

I think you need to use l'hopital's rule.

\[\lim_{x \rightarrow 0} \frac{ \cos(2x)-1 }{ 3x }\]

which would be 0/0, an indeterminite form, so using l'hospital's rule


\[\lim_{x \rightarrow 0}\frac{ -2\sin(2x) }{ 3 }\]

Since sin(2*0)= sin(0)=0, we get

\[\lim_{x \rightarrow 0} \frac{ -2(0) }{ 3 } = \frac{ 0 }{ 3 }\]

So, the limit is 0.