limx-0=13cscx^2-13cot^2

Question

use L'Hopital rule to find limit.

Answer 1

lim{x->0} 13csc(x^2) - 13cot(x^2)

= lim{x->0}13(csc(x^2) - cot(x^2))

= lim{x->0}13((1-cos(x^2))/(sin(x^2)), 0/0

= lim{x->0}13sin(x^2)(2x)/(cos(x^2) 2x), after using L'Hopital's rule

= lim{x->0}13tan(x^2)

= 0