Trig limits question

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Homework Statement


evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3


Homework Equations





The Attempt at a Solution


the answer in the textbook is 8/27
i figured they got that by raising 2 to the 3rd and 3 to the 3rd
but i'm not entirely sure what happens to the sin's

id really appreciate a worked out answer (that doesn't use l'hopital's rule)
 

Answers and Replies

  • #2
LCKurtz
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Homework Statement


evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3


Homework Equations





The Attempt at a Solution


the answer in the textbook is 8/27
i figured they got that by raising 2 to the 3rd and 3 to the 3rd
but i'm not entirely sure what happens to the sin's

id really appreciate a worked out answer (that doesn't use l'hopital's rule)

We don't do worked out answers. But here's a hint: Presumably you know something about the limit of sin(x)/x as x → 0. Make use of that by multiplying and dividing by certain powers of x.
 
  • #3
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We don't do worked out answers. But here's a hint: Presumably you know something about the limit of sin(x)/x as x → 0. Make use of that by multiplying and dividing by certain powers of x.

well
lim
x->0 sinx/x = 1
the problem is that i don't know how to apply it to this question
 
  • #4
LCKurtz
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well
lim
x->0 sinx/x = 1
the problem is that i don't know how to apply it to this question

What would be the limit of [itex]\frac {\sin(2x)}{2x}[/itex] as x → 0?
 
  • #5
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What would be the limit of [itex]\frac {\sin(2x)}{2x}[/itex] as x → 0?
that limit would be 1 as well
but i'm still not sure how it'd help
 
  • #6
LCKurtz
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that limit would be 1 as well
but i'm still not sure how it'd help

Now read the hint I gave in post #2 again. Hopefully you will see it; I'm signing off for tonight.
 

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