Determine the value of 'k' for which the following function is continuous at x=3: f(x) = (x+3)²/(x-3), x≠3; k, x=3

Function f is continuous at a point a if the following conditions are satisfied.

1. f(a) is defined
2. limx→af(x) exists
3. limx→af(x) = f(a)
   Now → limx→3(x+3)²/(x-3) = k
   so using L'hospital rule (differentiating on both sides i.e., denominator and numerator), we get
   2(x+3) = k
   Now substitute x=3 => k=12