Let k be a non - zero real number. If f x = ( e x − 1 ) 2 sin x k log 1 + x 4 , x ≠ 0 12 , x = 0 is a continuous function at x = 0 , then the value of k is

Question

Let k be a non - zero real number. If f x = ( e x − 1 ) 2 sin x k log 1 + x 4 , x ≠ 0 12 , x = 0 is a continuous function at x = 0 , then the value of k is, 2, 4, 3, 1

MARKS App · Accepted Answer

If the function is continuous then lim x → 0 f x = f 0 lim x → 0 ( e x − 1 ) 2 sin x k . log 1 + x 4 = 12 ⇒ lim x → 0 e x - 1 x 2 sin x k k . x k . log 1 + x 4 4 . x 4 = 12 ⇒ 1 1 k . 1 4 = 12 ⇒ 4 k = 12 ⇒ k = 3

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