Question

Materi : Limit
-Jawab dgn menggunakan cara-

Answer 1

Verified answer

Bab Limit
Matematika SMA Kelas XI

lim (1 - cos³ x) / (x tan x)
x→0
= lim (1 - cos x) (1² + 1 . cos x + cos² x)  / (x tan x)
  x→0
= lim ((1 - cos x) (1 + cos x + cos² x) (1 + cos x) / ((x tan x (1 + cos x)))
   x→0
= lim ((1 - cos² x) (cos² x + cos x + 1) / (x tan x (1 + cos x)))
   x→0
= lim ((sin² x) (cos² x + cos x + 1) / (x tan x (1 + cos x)))
  x→0
= lim (((sin² x) / (x tan x)) . ((cos² x  + cos x + 1) / (1 + cos x))
   x→0
= (cos² 0 + cos 0 + 1) / (1 + cos 0)
= (1 + 1 + 1) / (1 + 1)
= 3/2