If f x = x 4 + x - a x > 0 c x = 0 4 e 2 x + 3 e 1 x e 2 x + b e 1 x x < 0 is continuous at x = 0 for some constants a ,   b and c , then the value of 50 b a is equal to

Step-by-step solution

In l i m x → 0 + x 4 + x - a for 0 0 form a = 2 ⇒ l i m x → 0 + x 4 + x - 2 × 4 + x + 2 4 + x + 2 ⇒ l i m x → 0 + x 4 + x + 2 4 + x - 4 = l i m x → 0 + 4 + x + 2 = 4 Now, l i m x → 0 - f x = l i m x → 0 - 4 e 2 x + 3 e 1 x e 2 x + b e 1 x = l i m x → 0 + e 1 x 4 e 1 x + 3 e 1 x e 1 x + b = l i m x → 0 + 4 e 1 x + 3 e 1 x + b = 0 + 3 0 + b For f x to be continuous at x = 0 4 = 3 b ⇒ b = 3 4