I got 0 Limx rightarrow 0 + [lnx]sinx Solution as lim x->0 we have ln(0+) tends to negative infinity and sinx tends to zero so we have *0 form we multiply and divide by x lim x->0 (xlnx)*(sinx/x) we know as x->0+ sinx/x ->1 we need to determine where xlnx will go limx->0+ xlnx = limx->0+(lnx/(1/x)) apply L-hospital rule = limx->0+ (1/x)/(-1/x^2) = limx->0+ -x so it tends to 0 so product limx->0+ ln(x) sinx = limx->0+ (xlnx)*(sinx/x) = 1*0 = 0 so yes you are correct.