Lim x–3 3-x\3-√x+6

To find the limit of the given expression as x approaches -3, we can start by plugging in the value of x and simplifying the expression:

lim x→-3 (3 - x) / (3 - √x + 6)

Let's start by plugging in x = -3:

(3 - (-3)) / (3 - √(-3) + 6) (3 + 3) / (3 - i√3 + 6) 6 / (9 - i√3)

To simplify the expression further, we can multiply the numerator and denominator by the conjugate of the denominator:

6 / (9 - i√3) * (9 + i√3) / (9 + i√3) (6 * (9 + i√3)) / (81 - 3) (54 + 6i√3) / 78

Simplifying the expression further, we divide both the numerator and denominator by 6:

(54 + 6i√3) / 78 9 + i√3 / 13

So, the limit of the expression as x approaches -3 is 9 + i√3 / 13.