L'hopitals rule

Question

Use l'hopitals rule to solve:

Lim as x approaches π/2 of sec3x/sec5x

Answer 1

secant is the reciprocal of cosine, so sec(3x)/sec(5x) is equivalent to cos(5x)/cos(3x)

 

lim_x→π/2[sec(3x)/sec(5x)] = lim_x→π/2[cos(5x)/cos(3x)]  (has form 0/0)

 

   = lim_x→π/2[-5sin(5x)/(-3sin(3x))] (by L'Hopital's Rule)

 

   = -5(1)/(-3(-1)) = -5/3

Answer 2