Sine problem

ugatennis08

ugatennis08

ugatennis08

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Could somebody tell me what

sin(6x) / (6x)^3 = ?

I have done everything else in the question but I'm not sure what this part is equal to, I know sin(x)/x = 1 but how does that get applied here?
 
Umm, sin(x)/x does not equal 1.

Unless of course you're talking in the limit that x -> 0.
If so, I would suggest having a read up on l'Hopital's rule.
 
nearing infinity

nearing zero means it is not 0, say 0.0000001, now 0.00000001^3 = 0.00000000000000001 (ish), and 0.0000000001 / 1.0000000000000000000001 = 10000000000000 (ish) so if it is nearing zero for 'miles' then the resulting number is going to be nearing infinity

That is if you say x is nearing 0

the *6 doesn't really make much difference

so bassically, the really small x turns into really big y

not a clue what the answer is in algebraic format though
 
Last edited:
sin(x)/x -> 1 for x->0

sin(6x) / (6x)^3 = [ sin(6x)/(6x) ] / (6x)^2

in the limit x->0:
1/(6x)^2 -> inf
sin(6x)/(6x) -> 1

Therefore sin(6x)/(6x)^3 -> inf as x->0
(since we can use the product of two limits.)
 
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