Lim x–3 3-x\3-√x+6

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

lim x→-3 (3-x)/(3-√(x+6))

Substituting x = -3:

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

To evaluate this expression, we need to rationalize the denominator, which means getting rid of the square root in the denominator. We can do this by multiplying both the numerator and denominator by the conjugate of (3 - √3), which is (3 + √3):

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

Therefore, lim x→-3 (3-x)/(3-√(x+6)) = 3 + √3.