lim(x-0) x*log(sin x)=A) -1 B) log e1 C) 1 D) None of thesethe answer is Bplease explain me how - Maths - Limits and Derivatives

Question

lim(x-0) x*log(sin x)=A) -1 B) log e1 C) 1 D) None of thesethe
answer is Bplease explain me how

Anuradha Sharma · Accepted Answer

limx→0xlogsinx=limx→0logsinx1x And w can see that when we will put x = 0 it is ∞∞ form so, Using L'hospital rule, =limx→0ddxlogsinxddx1x=limx→01sin xddxsinx-1x2=limx→0cos xsin x-1x2=limx→0-x2cotx=0 as when x tends to o cotx tends to infinity but it is multiplied by zero so answer will be zero
So answer will be D But you have mentioned B as answer so
kindly recheck your query