Lim x–3 3-x\3-√x+6

To find the limit of the given function as x approaches -3, we substitute -3 into the function:

lim x→-3 (3 - x) / (3 - √(x + 6))

Plugging in -3:

= (3 - (-3)) / (3 - √(-3 + 6))

Simplifying:

= 6 / (3 - √3)

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

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

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

Expanding the denominator:

= (6 * (3 + √3)) / (9 - 3)

= (6 * (3 + √3)) / 6

Canceling out the 6's:

= 3 + √3

Therefore, the limit of the given function as x approaches -3 is 3 + √3.