Star
  • Star
the limit as x-> 0 for cos(2x)-1 / cos(3x)-1
Mathematics
schrodinger
  • schrodinger
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myininaya
  • myininaya
ok if you plug in 0 you get 0/0 so you can use l'hospital's rule -2sin(2x)/-3sin(3x) give me just a sec i'm going to use the equation thingy
myininaya
  • myininaya
\[\lim_{x \rightarrow 0}\frac{2}{3} \frac{\sin(2x)}{2x}\frac{\sin(3x)}{3x}6x^2\]
myininaya
  • myininaya
2/3(1)(1)(6)(0)=0

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Star
  • Star
it says the answer is 4/9
myininaya
  • myininaya
\[\lim_{x \rightarrow 0} \frac{\cos(2x)-1}{\cos(3x)-1}\]
myininaya
  • myininaya
is that right?
Star
  • Star
yep
myininaya
  • myininaya
ok let me see
myininaya
  • myininaya
oops i see a mistake
myininaya
  • myininaya
i put sin(3x) in the numerator do you see that?
myininaya
  • myininaya
\[\lim_{x \rightarrow 0}\frac{2}{3}\frac{\sin2x}{2x}\frac{3x}{\sin(3x)}\frac{2x}{3x}\]
myininaya
  • myininaya
2/3*1*1*2/3=4/9
myininaya
  • myininaya
got it? do you remember what sinx/x goes to as x goes to 0?

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