If lim x → 0 ⁡ 1 + p x + q x 2 c o s e c   x = 2048 , then the value of p 11 is equal to (take ln ⁡ 2 = 0 .69 )

Step-by-step solution

The given limit is of the form 1 ∞ ∴ e lim x → 0 ⁡ c o s e c   x 1 + p x + q x 2 - 1 = 2048 lim x → 0 ⁡ p x + q x 2 sin ⁡ x = ln ⁡ 2048 lim x → 0 ⁡ p x + q x 2 x ⋅ x sin ⁡ x = 11 ln ⁡ 2 lim x → 0 ⁡ p + q x 1 = 11 ln ⁡ 2 ⇒ p = 11 ln ⁡ 2 Hence, p 11 = ln 2 = 0 . 69