If the function f x = e k x − 1 tan k x 4 x 2 , x ≠ 0 16 , x = 0 is continuous at x = 0, then k = ….

Question

If the function f x = e k x − 1 tan k x 4 x 2 , x ≠ 0 16 , x = 0 is continuous at x = 0, then k = …., ± 1 8, ± 4, ± 2, ± 8

MARKS App · Accepted Answer

We have function, f x = e k x - 1 t a n k x 4 x 2 , x ≠ 0 16 , x = 0 is continuous at x = 0 ∴ l i m x → 0 f x = f 0 ⇒ l i m x → 0 e k x - 1 t a n k x 4 x 2 = 16 0 0 f o r m ⇒ l i m x → 0 e k x - 1 k x t a n k x k x × k 2 4 = 16 ⇒ k 2 4 = 16 ⇒ k 2 = 64 ⇒ k = ± 8

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