Question

Let f(x) = `{{:((tan pix)/(7x)";", x ≠ 0),("k"";", x = 0):}`. If f(x) is continuous at x = 0, then k = ______.

Options

• `pi/7`

• `7/pi`

• 1

• 0

Answer 1

Let f(x) = `{{:((tan pix)/(7x)";", x ≠ 0),("k"";", x = 0):}`. If f(x) is continuous at x = 0, then k = `pi/7`.

Explanation:

Since, f(x) is continuous at x = 0.

∴ f(0) = `lim_(x -> 0) "f"(x)`

⇒ k = `lim_(x -> 0) (tanpix)/(7x)`

⇒ k = `lim_(x -> 0) ((tan pix)/(pix)) * pi/7`

⇒ k = `(1)* pi/7`

⇒ k = `pi/7`