anonymous
  • anonymous
lim of x as sin(3x)/(2x) approaches 0
Mathematics
chestercat
  • chestercat
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agreene
  • agreene
try graphing it.
myininaya
  • myininaya
do you know how to evaluate \[\lim_{u \rightarrow 0}\frac{\sin(u)}{u}?\]
myininaya
  • myininaya
This limit should have been already introduced to you by the squeeze theorem (or at least this is the first way I learned what the above limit is) \[\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1\] commit this limit to memory it will be useful let's take this limit and see if i can give you a hint on how to do your problem since there is a 3x inside that sin let's let u equal 3x and if u goes to 0 then 3x goes to 0 since u=3x and since 3 doesn't go to 0 then the x must go to 0 so anyways \[\lim_{x \rightarrow 0}\frac{\sin(3x)}{3x}=1 \] try to use this limit here for your problem you may find it necessary to multiply by a 1 to do so

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