Question

lim x approaches 0^+ (sin(x))(ln 4x)

Answer 1

is this the limit of sin(x) * ln(4x) as x approaches 0?

Answer 2

yes

Answer 3

l'Hopital's rule again:

= limx->0 (ln(4x)/(1/sin(x)))

= limx->0 (1/x) / (-cosx*(sinx)^-2)

= limx->0 -(sinx)^2 / (x*cosx)

then apply l'hopital's again:

= limx->0 (-2*cosx*sinx) / (cosx - x*sinx)

= -2*1*0/(1 - 0)

= 0

Answer 4

thanks again: )