The value of a , so that lim x → 0 1 x 2 e a x - e x - x = 3 2 , is

Step-by-step solution

We have, lim x → 0 1 x 2 e a x - e x - x = 3 2 ⇒ lim x → 0 a e a x - e x - 1 2 x = 3 2 (using L 'Hospital rule to the left hand side) As x → 0 , the denominator is zero and as the value of the limit is finite so, numerator must be zero for x → 0 . Hence, a - 1 - 1 = 0 ⇒ a = 2 .