lim(x is going to 0) (sinh(2x))/(cosh(3x))

Question

lim_x=0(sinh(2x))

         (cosh(3x))

find the limit using l'hopital's rule

Answer 1

You cannot use L'Hopital's rule for the limit because it is not in 0/0 type or ∞/∞ type.

lim{x-->0} (sinh(2x))/(cosh(3x))

= lim{x-->0} (1/2)(e^(2x) - e^(-2x)) / [(1/2)(e^(3x) + e^(-3x))]

= 0/1

= 0