Question

find the lim as x approaches zero of 2-2cos(3x)/3x

Answer 1

do you know your limit laws?

Answer 2

some what

Answer 3

I guess you could apply L'Hospitals Rule. Did you learn his rule yet?

Answer 4

2-2cos(3x)=2(1-cos 3x)

Now apply 1-cos t formula

Answer 5

no I have not. I've only learned the basics. like when the numerator exponent is higher the lim does not exist and denominator degree is higher the lim is zero

Answer 6

Try what I said above.

Answer 7

Listen to aravinda

Answer 8

*Aravind

Answer 9

ok

Answer 10

I did that what's next?

Answer 11

What did you get?

Answer 12

2(1-COS3X)/3X from this point do I just plug in the zero?

Answer 13

That'll give me 0/0 which its not allowed

Answer 14

please help, I'm very clueless and I can't afford to fell that test tomorrow

Answer 15

Well, in general:
\[\lim_{x \rightarrow 0}\frac{ 1-cosx }{ x }=0\]As long as the x angle of cosine and the x int he denominator match, you can say its 0 and NOT undefined. So it looks like you just have 2*0 = 0

Answer 16

@have_sabr

Answer 17

That makes sense Thank you very much! :)

Answer 18

Yep, np :3

Answer 19

Given:
\[\lim_{x \rightarrow 0}\frac{2\cos(3x)}{3x}\]

Taking the RIGHT side limit we have:
\[\lim_{x \rightarrow 0^{+}}\frac{2\cos(3x)}{3x} = \infty\]

Taking the LEFT side limit we have:
\[\lim_{x \rightarrow 0^{-}}\frac{2\cos(3x)}{3x}= -\infty\]

Therefore, the two sided limit does not exist.