If f x = e 1 + 1 x - a e 1 x + 1 : x ≠ 0 b : x = 0 (where a and b are arbitrary constants) is continuous at x = 0 , then the value of a 2 is equal to (use e = 2 .7 )

Step-by-step solution

At x = 0 , LHL = l i m h → 0 + f 0 - h = l i m h → 0 + e 1 - 1 h - a e - 1 h + 1 = 0 - a 0 + 1 = - a RHL = l i m h → 0 + f 0 + h = l i m h → 0 + e 1 + 1 h - a e 1 h + 1 = l i m h → 0 e - e - 1 h × a 1 + e - 1 h = e and f 0 = b ∵ f x is continuous at x = 0 ∴ - a = e = b ⇒ a = - e a 2 = e 2