If lim x → ∞ ⁡ 1 + a x - 4 x 2 2 x = e 3 , then a is equal to

Step-by-step solution

lim x → ∞ 1 + a x - 4 x 2 2 x ( 1 ∞   form ) = e lim x → ∞ ⁡ 1 + a x - 4 x 2 - 1 2 x = e lim x → ∞ ⁡ 2 a - 8 x = e 2 a ∴   e 2 a = e 3 ⇒ 2 a = 3   ⇒     a = 3 2