Lim x–3 3-x\3-√x+6

To evaluate the limit of the given expression as x approaches -3, we can substitute x = -3 into the expression and simplify.

lim (x→-3) (3-x)/(3-√(x+6))

Substituting x = -3:

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

Now, to simplify further, we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:

6 * (3 + √3)/(3 - √3) * (3 + √3)/(3 + √3) (6 * (3 + √3)^2)/(9 - 3)

Expanding and simplifying:

(6 * (9 + 6√3 + 3))/(6) (54 + 36√3 + 18)/6 (72 + 36√3)/6 12 + 6√3

Therefore, the limit of the expression as x approaches -3 is 12 + 6√3.