Finding the limit

Question

Hi, Im really confused on how to find the following limits: 

 

a) lim_x→0   (csc(3x)/(sec(2x) 

 

 

b) lim_x→0  (tan(5x) / (6x)

Answer 1

a)csc(3x) is undefined at 0.  sec(2x) = 1 at 0.  Thus, the limit of the ratio is undefined.

b) use l,Hopital's rule.

lim x -> 0 5 sec²(5x)/6 = 5 * 1 / 6 = 5/6