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to get 4x in the denominator, 4x is multiplied in numerator and denominator.
got some idea?

Multiply the whole thing by (12x/12x).
rearrange.

you can also use L'Hopitals Rule
-Take derivative of both top and bottom, then reevaluate the limit

But it would be undefined if I took the limit of the bottom

Always with l'Hopital's. You'd think it was the only thing anyone ever retained from calc. class.

haha..yeah pretty much

I haven't learned it yet :(

|dw:1347162711646:dw|
got it now?

just use sin t / t when limit t->0 = 1 formula.

Why is it that .... the 4 is moved outside the limit?

multiplied by 4x in num and denom, and it can be seen,iguess

the 4 is constant and constants can be moved outside the limit

|dw:1347163083569:dw|

Sorry, I meant 4x

so 12x/sin3x

now 12x / sin 3x can again be written as 4 * (3x/sin 3x)
and using same limit again its 4*1= 4
ok?

|dw:1347163221313:dw|

Oh, I get it now!
Thank you guys SO MUCH!