f ( x ) = 72 x − 9 x − 8 x + 1 2 − 1 + cos ⁡ x , x ≠ 0 k log ⁡ 2 log ⁡ 3 , x = 0 Find the value of ' k ' for which the function f is continuous.

Step-by-step solution

Given that f ( x ) = 72 x − 9 x − 8 x + 1 2 − 1 + cos ⁡ x , x ≠ 0 k log ⁡ 2 log ⁡ 3 , x = 0 We know that f x is continuous ⇒ lim x → a f x   =   f a lim x → 0 72 x - 9 x - 8 x + 1 2 - 1 + cos x   = k   log 2 log 3 lim x → 0 9 x - 1 8 x - 1 2 - 1 + cos x × 2 + 1 + cos x 2 + 1 + cos x   = k   log 2 log 3 lim x → 0 9 x - 1 8 x - 1 2 - 1 - cos x × 2 + 1 + cos x 1   = k   log 2 log 3 ⇒ lim x &#