Question Number 115195 by bemath last updated on 24/Sep/20

lim_(x→(π/8))  ((cot 4x−cos 4x)/((π−8x)^3 )) ?

Answered by bobhans last updated on 24/Sep/20

let x = (π/8)+p ; p→0  lim_(p→0)  ((cot (4p+(π/2))−cos (4p+(π/2)))/((−8p)^3 )) =  lim_(p→0)  ((−tan 4p+sin 4p)/(−512p^3 )) =   lim_(p→0)  ((tan 4p−sin 4p)/(512p^3 )) = lim_(p→0)  ((tan 4p(1−cos 4p))/(512p^3 ))  = ((4×8)/(64×8)) = (1/(16))