Whats the solution for: the limit of x * cotx as x approaches 0?

Question

Whats the solution for: the limit of x * cotx as x approaches 0?

Answer 1

the answer is " 1 "...{x / sin x} { cos x}-----> 1 * 1

Answer 2

limit x--->0 x*cot x

= limit x------>0 x* cos x/sin x

=limit x------->0 (cos x - x sin x)/cos x

by l'hospital rule,

(1 - 0)/1

=1

Answer 3

lim x → 0 x*cotx

= lim x → 0 x*cosx / sinx

= lim x → 0 (cosx - xsinx) / cosx (using L'Hospital's theorem)

= (1 - 0) / 1

= 1.