A) lim f(x) &
as x approches -2+
Since in the interval -2 <= x <= 1, or [-2,1], the f(x) is not defined, then as x approaches -2 from the right, it is stopped from moving beyond x=1, where f(x) = f(1) = sqrt(1+2) = sqrt(3).
Therefore the limit is sqrt(3).
B) Lim f(x)
as x approaches -2-
As x approaches -2 from the left, the limit of f(x) is the intersection of f(x) = x+3 and the vertical line x = -2
f(x) = x+3, and when x = -2, f(x) = -2 +3 = 1.
Therefore, the limit is 1.