If lim x → 0 1 x 8 1 − cos x 2 2 − cos x 2 4 + cos x 2 2 cos x 2 4 = 2 − k then the value of k is

Step-by-step solution

lim x → 0 1 x 8 1 − cos x 2 2 − cos x 2 4 + cos x 2 2 cos x 2 4 = lim x → 0 1 − cos x 2 2 1 − cos x 2 4 x 8 = lim x → 0 1 − cos x 2 2 x 4 × 1 − cos x 2 4 x 4 = lim x → 0 1 − cos x 2 2 4 × x 4 4 × 1 − cos x 2 4 16 × x 4 16 Using lim x → 0 1 - cos x x 2 = 1 2 = 1 2 × 1 4 × 1 2 × 1 16 = 1 256 = 2 - 8 ⇒ 2 - 8 = 2 - k       ⇒ k = 8