Question

If the function f defined as

`f(x) = {{:((x^2  -  9)/(x  -  3)",", x ≠ 3),(k",", x = 3):}`

is continuous at x = 3, find the value of k.

Answer 1

Here f is continuous at x = 3, then `lim_(x -> 3) f(x) = f(3)`

⇒ `lim_(x -> 3) ((x - 3)(x + 3))/((x - 3)) = k`

⇒ 3 + 3 = k

⇒ k = 6