Question

If the function

f(x) = `(("e"^"kx" - 1)tan "kx")/"4x"^2, x ne 0`

= 16 , x = 0

is continuous at x = 0, then k = ?

विकल्प

• `+- 1/8`

• ± 4

• ± 2

• ± 8

Answer 1

± 8

Explanation:

We have function,

f(x) = `(("e"^"kx" - 1)tan "kx")/"4x"^2, x ne 0`

= 16 , x = 0

is continuous at x = 0

`therefore lim_(x -> 0) "f"(x) = "f"(0)`

`=> lim_(x -> 0) (("e"^"kx" - 1)/"kx")((tan "kx")/"kx") xx "k"^2/4 = 16`

`=> "k"^2/4 = 16`

⇒ k² = 64

⇒ k = ± 8