Question

lim x->0 [(3sin4x)/(sin 3x)] = 4 lim x->0 [(sin 4x/4x)x(3x/sin3x)]

How is this true?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

haha..yeah pretty much

Answer 7

I haven't learned it yet :(

Answer 8

They're learning about sinc(x) here anyway ... that's a few lectures before the class on l'Hopital's.

Answer 9

got it now?